®l?f  1.  B.  Bill  ICibrarg 


TL670 


This  book  is  due  on  the  date  indicated 
below  and  is  subject  to  an  overdue 
fine  as  posted  at  the  circulation  desk. 


EXCEPTION:  Date  due  will  be 
earlier  if  this  item  is  RECALLED. 


wR'«% 


AIRPLANE 
DESIGN  AND  CONSTRUCTION 


AIRPLANE 
DESIGN  AND  CONSTRUCTION 


BY 
OTTORINO    POMILIO 

CONSULTING    AERONAUTICAL   ENGINEER    FOR   THE    POMILIO  BROTHERS   CORPORATION 


First  Edition 
Fifth  Impression 


McGRAW-HILL  BOOK  COMPANY,  Inc. 

NEW   YORK:    370   SEVENTH   AVENUE 
LONDON:    6  &  8  BOUVERIE  ST.,  E.  C.  4 

1919 


Copyright,  1919,  by  the 
McGraw-Hill  Book  Company,  Inc. 


PRINTED   IN   THE    UNITED   STATES    OF   AMERICA 


THE   MAPLE   PRESS   COMPANY,   YORK,   PA. 


ilJitir  nnis  (!^)rbilU  Brigljl 


65924 


INTRODUCTION 

By  far  the  major  part  of  experimental  work  in  aero- 
dynamics has  been  conducted  in  Europe  rather  than  in 
America,  where  the  feat  of  flying  in  a  heavier  than  air  ma- 
chine was  first  accomplished.  This  book  presents  in  greater 
detail  than  has  hitherto  been  attempted  in  this  country  the 
application  of  aerodynamic  research  conducted  abroad  to 
practical  airplane  design. 

The  airplane  industry  is  now  shifting  from  the  design  and 
construction  of  military  types  of  craft  to  that  of  pleasure 
and  commercial  types.  The  publication  of  this  book  at 
this  time  is,  therefore,  opportune,  and  it  should  go  far 
toward  replacing  by  scientific  procedure  many  of  the  "cut 
and  try"  methods  now  used.  Employment  of  the  data 
presented  should  enable  designers  to  save  both  time  and 
expense.  The  arrangement,  presentation  of  subject  matter, 
and  explanation  of  the  derivation  of  working  formulae, 
together  with  the  assumptions  upon  which  they  are  based, 
and  consequently  their  limitations,  are  such  that  the  book 
lends  itself  to  use  as  a  text  in  technical  schools  and  colleges. 

The  dedication  of  this  volume  to  Wilbur  and  Orville 
Wright  is  at  once  appropriate  and  significant;  appropriate, 
in  that  it  is  a  tangible  expression  of  the  keen  appreciation 
of  the  author  for  the  great  work  of  these  two  brothers; 
and  significant,  in  that  it  is  a  return,  in  the  form  of  a  rational 
analysis  of  many  of  the  problems  relating  to  airplane  design 
and  operation,  on  the  part  of  the  product  of  an  older  civili- 
zation to  the  product  of  the  new,  as  a  sort  of  recompense 
for  the  daring,  courage  and  inventive  genius  which  made 
human  flight  possible. 

J.  S.  Macgregor. 

New  York,  1919. 


CONTENTS 


Introduction 


Paoe 
.     vii 


Chapter 

I. 

II. 

III. 

IV. 
V. 
VI. 


VII. 

VIII. 

IX. 

X. 

XL 


PART   I 
Structure  of  the  Airplane 

The  Wings 1 

The  Control  Surfaces 19 

The  Fuselage 37 

The  Landing  Gear 44 

The  Engine 51 

The  Propeller 72 

PART  II 

The  Airplane  in  Flight 

Elements  of  Aerodynamics 87 

The  Glide 102 

Flying  with  Power  On 115 

Stability  and  Maneuverability 134 

Flying  in  the  Wind 151 


PART  III 
The  Efficiency  of  the  Airplane 

XII.     Problems  of  Efficiency 161 

XIII.  The  Speed 167 

XIV.  The  Chmbing 188 

XV.     Great  Loads  and  Long  Flights 204 

PART  IV 
Design  of  the  Airplane 

XVI.  Materials 221 

XVII.  Planning  the  Project 261 

XVIII.  Static  Analysis  of  Main  Planes  and  Control  Surfaces   ....  276 
XIX.  Static  Analysis  of  Fuselage,  Landing  Gear  and  Propeller .    .    .  324 

XX.     Determination  of  the  Flying  Characteristics 358 

XXI.     Sand  Tests— Weighing— Flight  Tests 379 

Index 401 


ACKNOWLEDGMENT 

The  author  desires  to  express  his  sincere  thanks  to  Mrs. 
Lester  Morton  Savell  for  her  valuable  assistance  in  matters 
pertaining  to  English  and  to  Mr.  Garibaldi  Joseph  Piccione 
for  his  intelligent  assistance  in  drawing  the  diagrams. 

O.P. 


AIRPLANE  DESIGN 

AND 

CONSTRUCTION 


PART  I 
STRUCTURE  OF  THE  AIRPLANE 


CHAPTER  I 
THE  WINGS 

While  for  birds,  and  in  general  for  all  animals  of  the  air, 
wings  serve  to  insure  both  sustentation  and  propulsion, 
those  of  the  airplane  are  used  solely  to  provide  the  means 
of  sustaining  the  machine  in  the  air. 

The  phenomenon  of  sustentation  is  easily  explained.  A 
body  moving  through  the  air  produces,  because  of  its  mo- 
tion, a  disturbance  of  the  atmosphere  which  is  more  or  less 
pronounced  and  complex  in  character.  In  the  final  analy- 
sis, this  disturbance  is  reduced  to  the  formation  of  zones 
of  positive  and  negative  pressures.  The  resultant  of  these 
pressures  may  then  be  classified  into  its  three  components : 

1.  Vertical  or  sustaining  force,  called  Lift, 

2.  Horizontal  component  parallel  and  opposite  the  line 
of  flight,  called  Drag,  and 

3.  Horizontal  component  perpendicular  to  the  line  of 
flight,  called  Lateral  Drift. 

The  vertical  component  may  be  positive  or  negative. 
An  example  of  the  negative  component  is  found  in  the 
elevator  used  for  the  climbing  maneuver  of  an  airplane, 
as  will  be  shown  later. 

1 

Library 
N„  C.  State  College 


2  AIRPLANE  DESIGN  AND  CONSTRUCTION 

The  horizontal  component  parallel  to  the  line  of  flight, 
is  always  negative;  i.e.,  it  tends  to  retard  the  motion  of 
the  body.  "Conservation  of  energy"^  is  the  principle 
underlying  this  phenomenon. 

The  horizontal  component  perpendicular  to  the  line  of 
flight  is  called  the  force  of  "drift,"  because  it  tends  to 
make  the  body  drift  from  the  Une  of  flight.  This  compo- 
nent, generally  not  existing  in  normal  flight,  is  of  great 
importance  in  the  directional  maneuvers  of  airplanes. 

For  a  body  having  a  plane  of  symmetry  and  moving 
through  space  so  that  the  line  of  flight  is  contained  in  that 
plane,  the  force  of  drift  is  zero  and  the  only  components 
acting  are  the  lift  and  the  drag. 

Observations  made  of  birds'  wings  and  results  based 
upon  the  experiences  of  experimenters  in  aeronautics,  have 
demonstrated  the  possibility  of  devising  surfaces  of  such 
form  that  by  properly  moving  them  through  the  air  they 
create  reactions,  of  which  the  vertical  component  has  a  far 
greater  magnitude  than  the  horizontal. 

Thus,  a  surface  capable  of  developing  high  values  of  lift 
with  small  values  of  drag  is  called  a  wing. 

In  actual  practice,  as  will  be  shown  further  on  in  a  more 
detailed  study  of  aerodynamical  principles  (Chapter  7),  the 

value  of  the  ratio  j^ —  varies  from  15  to  23.     This  means 

that  wings  may  be  built,  which,  for  every  23  lb.  of  load 
carried,  offer  a  resistance  to  motion  of  but  I  lb.  It  is 
natural,  then,  that  designers  direct  all  efforts  toward  in- 
creasing the  y^ —  ratio,  which  is  used  to  define  the  efficiency 

of  the  wing.     Three  factors  influence  such  efficiency: 

the  profile  of  the  wing  section, 

the  ratio  of  the  wing  span  to  its  depth  or  chord  (called 
the  Aspect  Ratio),  and 

1  This  principle  states  that  energy  can  be  neither  created  nor  destroyed. 
If  the  horizontal  component  were  positive,  perpetual  motion  would  ensue, 
since  it  would  be  necessary  only  to  furnish  the  initial  force  to  set  the  body  in 
motion.  The  body  would  then  continue  in  its  path  without  further  applica- 
tion of  energy. 


THE  WINGS  3 

the  relative  position  of  the  wings  (in  multiplane  ma- 
chines). 

The  profile  of  a  wing  section  is  its  major  section  at  right 
angles  to  the  span  of  the  wing.  Because  of  the  simplicity 
of   modern    construction,   wings  are  generally  built  with 


Leadinq/ 
^Edse  ^ 


Back. 


Bo+1-or 


Fig.   1. 


a  constant  section  throughout  the  span.  In  the  early 
days  of  aeronautics,  however,  many  types  of  wings  were 
built  with  a  variable  wing  section,  but  the  aerodynamical 
advantages  derived  from  their  use  were  never  sufficient  to 
compensate  for  the  complicated  construction  required. 

In  the  profile  of  a  wing,  there  are  the  following  distinct 
elements  (Fig.  1) :  leading  edge,  back,  bottom  and  trailing 
edge.     The  proper  use  of  these  elements  makes  it  possible 

to  obtain  the  highest  values  of  the  y^ ratio,  as  well  as  to 

vary  the  Lift  coefficient  according  to  the  load  to  be  carried 
per  square  foot  of  wing  surface. 


Line  of  Fl.gh+. 


The  angle  between  the  wing  chord  and  the  line  of  flight, 
called  the  angle  of  incidence  of  the  wing  (Fig.  2),  may  vary 
between  greater  or  smaller  limits.  As  a  result,  the  distri- 
bution and  value  of  the  positive  and  negative  pressures 

will  vary,  and  give  different  values  of  Lift,  Drag  and  t^ 

The  laws  of  variation  of  these  factors  are  rather  complicated 
and  cannot  be  expressed  by  means  of  formulae.  It  is  pos- 
sible,  however,  to  express   them  by  mea.ns  of  curves  as 


4  AIRPLANE  DESIGN  AND  CONSTRUCTION 

illustrated  in  Figs.  3  and  4.  These  illustrate  the  laws  of 
variation  for  the  values  of  the  Lift,  Drag  and  yz — -  coeffi- 
cients for  two  types  of  aerofoils,  which,  although  having  the 
same  lengths  of  chord,  differ  in  other  elements. 

It  is  now  necessary  to  introduce  a  new  factor,  namely, 
the  speed  or  velocity  of  translation  of  the  wing. 

All  aerodynamical  phenomena,  when  considered  with 
respect  to  speed,  follow  the  general  law  that  the  intensity 
of  the  phenomenon  increases  not  in  proportion  to  the  speed, 
but  to  the  square  of  the  speed.  This  is  accounted  for  by 
the  fact  that  for  redoubled  speed  not  only  is  the  velocity 
of  impact  of  air  molecules  against  the  body  moving  in  the 
air  redoubled,  but  so  also  is  the  number  of  molecules  that 
are  struck  by  the  body.  Consequently  it  is  seen  that  the 
intensity  of  the  phenomenon  is  quadrupled. 

Assuming  a  wing  with  an  area  of  A  square  feet,  the  fol- 
lowing general  equations  may  be  written : 


(1) 


L  =  X  X  .4  X  V 
D  =  8X  A  XV'~ 
where 

L  =  total  Lift  for  area  A  in  pounds 
D  =  total  Drag  for  area  A  in  pounds 
V  =  speed    of    translation    in    miles    per    hour 
(m.p.h.). 

In  practice  it  is  convenient  to  refer  the  coefficients  X  and 
8  to  the  velocity  of  100  m.p.h.,  whence  the  equation  (1) 
becomes 

L  =  X  X  A  X  (4)^ 

IS  A  =  I  sq.  ft.,  and  V  =  100  m.p.h.,  then 
Li  =  X 


(2) 


that  is,  X  is  the  load  in  pounds  carried  by  a  wing  with  an 
area  of  1  sq.  ft.  and  moving  at  a  velocity  of  100  m.p.h., 


THE  WINGS 


8    X 

1.75  35 


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Fig.  3. 


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degrees. 

FlQ.  4. 


6  AIRPLANE  DESIGN  AND  CONSTRUCTION 

and  8  the  head  resistance  in  pounds  for  a  wing  with  an 
area  of  1  sq.  ft.  and  moving  at  a  velocity  of  100  m.p.h. 
Knowing  X  and  5,  by  using  equation  (2)  the  values  of  L  and 
D  may  be  found  for  any  area  or  any  speed.     Also,  the 

ratio  -  is  equal  to  y:  which  is  obtained  by  dividing  the  L 

0  U 

equation  by  the  D  equation. 

Now,  the  coefncicnts  X  and  b  may  assume  an  entire 
series  of  varied  values  by  changing  the  angle  of  incidence 
of  the  wings.     Figs.  3  and  4  show  the  laws  of  variation 

of  X,  5  and  -  for  tw^o  different  types  of  wings  to  which  we 

0 

will  refer  as  wing  No.  1  and  wing  No.  2. 

An  examination  of  the  diagrams  is  instructive  because  it 
shows  how  it  is  possible  to  build  wings  which  may  have 
totally  different  values  of  Lift,  the  speed  being  the  same  for 
both  wings.  For  example,  at  an  angle  of  incidence  of  3°, 
wing  No.  1  gives  X  =  11.8,  while  wing  No.  2  gives  X  =  17.6; 
in  other  w^ords,  with  equal  speeds,  wing  No.  2  carries 
a  load  49  per  cent,  greater  than  wing  No.  1. 

The  laws  of  variation  of  X  and  5  depend  upon  the  several 
elements  of  the  wing,  namely,  the  leading  edge,  top,  bottom 
and  trailing  edge.  Let  us  consider  separately  the  function 
of  each  of  these  elements: 

Actually,  the  function  of  the  leading  edge  is  to  penetrate 
the  air  and  to  deviate  it  into  two  streams,  one  w^hich  will 
pass  along  the  top  and  the  other  which  will  pass  along  the 
bottom  of  the  wing.  In  order  to  obtain  a  good  efficiency 
it  is  necessary  that  this  penetration  be  made  with  as  little 
disturbance  as  possible,  in  order  to  prevent  eddies.  Eddies 
give  rise  to  considerable  head  resistance  and  are  therefore 
great  consumers  of  energy.  For  that  reason,  the  leading 
edge  should  be  designed  with  the  same  criterions  as  those 
adopted  in  the  design  of  turbine  blades.  Figs.  5  and  6 
show  the  phenomenon  schematically.  Due  to  inertia, 
the  air  deviated  above  the  wing  tends  to  continue  in  its 


THE  WINGS 


rectilinear  path,  thus  producing  a  negative  pressure  or 
vacuum  on  top  of  the  wing.  This  negative  pressure  exerts 
a  centripetal  force  on  the  air  molecules,  tending  to  deflect 


Fig. 


-Leading  edge  of  good  efficiency. 


their  path  downward  so  as  to  flow  along  the  top  curvature 
of  the  wing.  A  dynamic  equilibrium  is  thereby  established 
between  the  negative  pressure  and  the  centrifugal  force  of 


Fig.   G. — Leading  edge  of  poor  efficiency. 

the  various  molecules  (Fig.  7).  It  is  obvious,  then,  that 
the  top  curvature  has  a  pronounced  influence  not  only  upon 
the  intensity  of  the  vacuum,  but  also  on  the  law  of  negative 
pressure  distribution  along  its  entire  length. 


POSITIVE     PRESSURE. 
Fig.  7. 


The  air  deviated  below  the  wing  tends  instead,  also  due 
to  inertia,  to  condense,  thus  producing  a  positive  pressure 
which  forces  the  air  molecules  to  follow  the  concavity  of 


8 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


the  bottom  curvature.  Because  of  this  change  in  the  direc- 
tion of  velocities,  a  centrifugal  force  is  developed  which  is 
in  dynamic  equihbrium  with  the  positive  pressure  produced 
TFig.  7). 

Curves  showing  the  laws  of  distribution  of  the  positive 
and  negative  pressures  are  given  in  Fig.  8.     The  resultant 


-6 

/^ 

N. 

-  5 

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-  4 

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-  3 

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y 

+  2 

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1.1 

Lb.per 

Sq.Ft. 

^ 

+  3 

\ 

-      y 

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V^ 

^ 

Fig.  8. 


of  these  pressures  represents  the  value  -r-     It  will  be  noted 

that  the  portion  of  the  sustentation  due  to  the  vacuum 
above  is  much  greater  than  that  due  to  the  positive  pressure 
below.  In  the  case  under  consideration,  it  is  2.9  times 
greater,  and  equal  to  74  per  cent,  of  the  total  Lift,  There- 
fore, the  study  of  the  top  curvature  must  be  given  more 
careful  consideration  than  that  of  the  bottom  curvature,  as 
a  wing  is  not  at  all  defined  by  the  bottom  curvature  alone. 
In  practice,  the  means  adopted  to  raise  the  value  of  X  is 


THE  WINGS  9 

to  increase  both  the  convexity  of  the  top  and  the  concavity 
of  the  bottom  of  the  wing,  thereby  increasing  the  intensi- 
ties of  the  negative  and  positive  pressures. 

The  traiUng  edge  also  has  its  bearing  on  the  efficiency. 
Its  shape  must  be  such  as  to  straighten  out  the  air  stream- 
liness  when  the  air  leaves  the  wing,  affecting  a  smooth, 
gradual  decrease  in  the  negative  and  positive    pressures 


Fig.  9. — Trailing  edge  of  good  efficiency. 

until  their  difference  becomes  zero.  In  this  manner,  the 
formation  of  a  wake  or  eddies  behind  the  wing,  with  the 
resulting  losses  of  energy,  is  avoided  (Figs.  9  and  10). 

In  brief,  for  good  wing  efficiency,  it  is  primarily  necessary 
for  the  leading  and  trailing  edges  to  be  of  a  design  which  will 
avoid  the  formation  of  eddies,  and  in  order  to  obtain  a 
higher  value  of  the  Lift  coefficient  X  the  top  and  bottom 
curvatures  must  be  increased. 


Fig.   10. — Trailing  edge  of  poor  efficiency. 

From  the  foregoing  it  is  easy  to  understand  the  impor- 

S 
tance  of  the  ratio  ^ ;  that  is,  the  relation  between  the  span 

S  and  the  chord  C  of  a  wing. 

Considering  the  front  view  of  a  wdng  surface.  Fig.  1 1 ,  which 
represents  a  section  parallel  to  the  leading  edge,  and  shows 
the  mean  negative  and  positive  pressure  curves  for  the  top 
and  bottom  of    the  wing,  it   will   be   seen   that  while  in 


10 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


the  central  part  the  curves  are  represented  by  hnes  parallel 
to  the  wing,  at  the  wing  tips  A  and  B,  they  suffer  serious 
disruption,  for  at  the  end  of  the  wing  a  short  circuit  between 
the  compression  and  the  depression  occurs.  This  is  due 
to  the  air  under  pressure  rushing  toward  the  vacuum  zone, 
thus  establishing  an  air  flux  (the  so-called  marginal  losses) , 
with  the  result  that  at  the  wing  tips  the  average  pressure 
curves  come  together,  and  the  Lift  is  decreased  consider- 
ably, thus  lowering  the  value  X  of  the  wing.     It  is  therefore 


Nega+i 


ve      Pressure 


Posi  +  ive     Pressure 


necessary  to  reduce  the  importance  of  this  phenomenon 
to  a  minimum,  this  being  done  by  increasing  the  ratio  of 

the  span  to  the  chord  (  ts  )  • 

Assume,  as  it  is  sometimes  done  in  practice,  that  the 
disruption  in  the  average  curves  due  to  marginal  losses 
extends  for  a  distance  AC  and  BD,  equal  to  the  chord  of 
the  wing;  and  also  that  the  diagram  is  modified  according 
to  a  linear  law.  This  is  equivalent  to  assuming  a  decrease  in 
the  Lift  measured  by  the  triangles  AA'C,  AA"C",  BB'D' 
and  BB"  D" .  The  same  result  is  obtained  as  though  the 
average  X  remained  constant  and  the  lifting  surface  were  re- 
duced by  the  amount  c-,  which  means  that  the  total  surface 
would  be  reduced  by  sXc  —  c'^.  If  the  product  sXc  is  kept 
constant  by  increasing  s  and  diminishing  c  correspondingly, 
the  importance  of  the  term  c  is  greatly  decreased.     The  loss  is 

c~  c 

expressed  by  -^v,—  =  -'  that  is,  by  the  inverse  of  the  ratio 
S  /\  c        s 


THE  WINGS 


11 


So  it  is  seen  that  by  increasing  the  ratio  ->  the 


span 
chord 

average  value  of  the  coeffi- 
cient of  Lift  is  increased,  and 
it  is  therefore  advantageous 
to  build  wings  of  large  spread. 
In  practice,  however,  there  is 
a  limit  beyond  which  this  ad- 
vantage becomes  a  minimum, 
and  there  are  also  static  and 
structural  problems  to  be  con- 
sidered which  limit  the  value 


of   the  ratio 


In   modern 


Fig.    12. 


machines,  this  value  varies 
from  5  to  12,  and  even  more. 
In  biplanes,  triplanes  and 
multiplanes,  another  very  im- 
portant problem  is  presented ; 
that  of  the  mutual  interference  of  each  plane  upon  the 
others.  In  view  of  the  close  arrange- 
ment of  the  surfaces  necessitated  by 
structural  considerations,  and  the 
high  values  of  their  negative  and 
positive  pressures  of  air,  a  conflic- 
tion  of  air  flow  is  formed  over  the 
entire  wing  surface,  with  the  result 
that  the  value  of  the  Lift  coefficient 
is  lowered.  Figs.  12  and  13  illus- 
trate this  phenomenon  for  a  biplane 
and  triplane  respectively.  In  the 
case  of  the  biplane,  the  following 
effects   ensue : 

1.  Decrease  in  vacuum  on  top  of 
lower  plane,  and 

2.  Decrease  in  positive  pressures 
on   bottom   of  upper  plane. 

Fig.  13.-Triplane  system.  J^    ^^^    ^^^^    o£     ^j^^     triplane,     the 

losses  are  still  greater,  due  to 


12  AIRPLANE  DESIGN  AND  CONSTRUCTION 

1.  Decrease  in  vacuum  on  top  of  bottom  plane, 

2.  Decrease  in  positive  pressures  on  bottom  of  inter- 
mediate plane, 

3.  Decrease  in  vacuum  on  top  of  intermediate  plane,  and 

4.  Decrease  in  positive  pressures  on  bottom  of  upper 
plane. 

It  is  thus  seen  how  undesirable,  from  an  aerodynamical 
point  of  view,  the  triplane  really  is.  At  the  present  time, 
however,  the  triplane  is  not  a  common  type  of  airplane,  so 
the  discussion  here  will  be  limited  to  the  biplane. 

Another  important  ratio  in  aeronautics  is  the  unit  load 
on  the  wings,  or  the  number  of  pounds  carried  per  square 
foot  of  wing  surface.  Theoretically  this  value  may  vary 
between  wide  limits;  for  example,  for  wing  No.  2  set  at  an 
angle  of  6°  and  moving  at  a  speed  of  150  miles  an  hour,  the 
ratio  is  51  lb.  per  sq.  ft.  In  practice,  however,  that  value 
has  never  been  reached.  Special  racing  airplanes  have 
been  built  whose  unit  loads  were  as  high  as  13  lb.  per 
sq.  ft.,  but  the  principal  disadvantages  of  such  high  unit 
loads  are  the  resulting  high  gliding  and  landing  speeds,  and 
an  appreciable  loss  in  maneuverability.  For  this  reason 
designers  strive  to  confine  the  unit  load  between  the  limits 
of  6  and  8  lb.  per  sq.  ft. 

Consider  a  biplane  with  a  chord  and  gap  each  of  6  ft. 
with  a  unit  load  equal  to  8  lb.  per  sq.  ft.  Keeping  in  mind 
what  has  been  previously  stated  (Fig.  8),  it  can  be  as- 
sumed that  the  values  of  positive  and  negative  pressures 
(vacuum)  found  at  the  top  and  bottom  of  both  wings  would 
be  equal  to  2  lb.  per  sq.  ft.  and  6  lb.  per  sq.  ft.  respectively, 
provided,  of  course,  that  the  two  wing  surfaces  had  no  effect 
on  each  other.  Now,  if  a  difference  in  pressure  of  8  lb. 
per  sq.  ft.  is  produced  between  two  points  in  the  air  at  a 
distance  of  6  ft.  from  each  other,  the  air  under  pressure 
rushing  violently  to  fill  up  the  vacuum  will  result  in  a  veri- 
table cyclone  in  the  intervening  space. 

When  a  wing  is  in  motion,  condensed  and  rarefied 
conditions  of  the  air  are  being  constantly  produced,  so  that 


THE  r/INGS 


13 


.15  35 


_     ___ 

~r                                    n^ 

i      ■                        ^ 

X                                       1          ^ 

1  50  ?0 

J_                             > 

-L                       y- 

1  1                         / 

1 ?5  25       1                                             1                             III              / 

1       ■                                 1                         Ml/ 

1                                        1     1                         y'^           1 

1                                         "T                         1   1         1     /          1 

1                                                                      1   1         1    /             1 

1  on  ?n       1     1                              !                       1  1       J/             ' 

'■""  ^0                                         1                       \  \      ^              1 

>^'                    oJ     /-^     1             ^ 

JiS          -IV   4- 

«-■■             /       '              / 

07^   15                         1                                 ^    '       N>.     /             1               ^^ 

■                                4I       Z    _L       5^          ±       ^^    1 

/      ±       ^^^^    ±^^         i 

^                «^              ^-^                L 

y^            ^^^^               -t 

0.50  10  — L_L-^ Lyj^_^::_^^__::s     __i_ 

::::::::::::#:i::;?::::::::::  ::s-: 

nz     ^^                              ^. 

zL^y 

nor'     c             1                                               />n 

0.25    b       -^                           ^-'^ 

^^^ 

^"^        ? 

0                               2 

25 


22.5 


17.5 


12,5 


15 


-3-2-1        0        1        234       5e7&9 
Degrees. 

Fig.   14. 

8    A,  2V, 

S 

25 


22.5 


■  .Iw-          ^^ 

' 

1.50   30  . 

/ 

f 

/ 

/ 

/ 

1.25   25  . 

i 

/■ 

Ub 

.a, 

/ 

'<" 

/ 

s 

. 

b 

/ 

1 00  20  - 

s. 

/ 

1 

N 

/ 

s 

Jf 

- 

) 

/V, 

^' 

1 

J 

> 

0.75  15 : 

V 

^ 

/' 

s 

,^ 

s 

^ 

i 

1 

<> , 

X 

SI 

/ 

1 

y^ 

"  , 

0.50   10  - 

1 

11^ 

>y 

s 

-- 

— 

_ 

- 

- 

— 

5^ 

y 

_ 

_ 

_ 

_ 

- 

-— 

r 

— 

■ 

- 

- 

V 

— 

- 

- 

- 

- 

f 

y 

0.25     5  . 

1 

y  "j 

^ 

f 

f 

1 

0 : 

L 

- 

20 


17.5 


12.5 


75 


3    -2     -I        0        1        2       3       4       5       6       7       6      .9 
Degrees. 
Fig.   15. 


14  AIRPLANE  DESIGN  AND  CONSTRUCTION 

a  certain  dynamic  equilibrium  ensues.  In  order  to  study 
the  phenomenon  more  closely,  a  few  brief  computations  will 
be  made. 

Again  consider  the  type  of  wing  curve  whose  characteris- 
tics are  given  in  Fig.  3,  and  assume  that  it  is  to  be  adopted 
for  a  biplane.  In  such  a  case,  the  curves  in  Fig.  3  are  no 
longer  applicable  and  new  curves  must  be  determined 
experimentally,  since  the  aerodynamical  behavior  of  the 
wing  shown  in  Fig.  3  will  change  for  every  one  of  the  three 
following  conditions : 

1.  Acting  alone,  as  for  a  monoplane, 

2.  Serving  as  the  upper  plane  of  a  biplane  structure,  and 

3.  Serving  as  the  lower  plane  of  a  biplane  structure. 
Fig.  14  gives  the  characteristics  for  wing  No.  1  serving  as  a 
lower  plane.  Considered  as  an  upper  plane,  the  aerody- 
namical curve  is  practically  the  same  as  that  in  Fig.  3. 
Fig.  15  gives  the  characteristics  of  a  complete  biplane 
whose  upper  and  lower  planes  are  similar. 

Compare  now  a  monoplane  having  a  wing  surface  of  200 
sq.  ft.,  possessing  the  type  of  wing  mentioned  above,  with 
a  biplane  also  having  the  same  wing  section,  and  whose 
planes  are  each  100  sq.  ft.  in  area.  Assume  each  machine 
to  carry  a  load  of  1500  lb.  at  a  speed  of  100  miles  per  hour. 
The  problem  then  is  to  find  the  values  of  the  angles  of  inci- 
dence and  the  thrust  efforts  required  to  overcome  the  Drag. 

From  the  equation 

X  XA  X'   ^ 


,100 
smce 

L  =  1500  lb.  and 

A  =  200  sq.  ft., 
then 

X-^^^^  -75 
'^  -  -20-0   -  ^'^ 

which  value  of  X  gives,  for  the  monoplane  (Fig.  3), 

i  =  r 

5  =  0.415 
D  =  0.415  X  200  =  83  lb. 


THE  WINGS  15 

and  for  the  biplane  (Fig.  15), 

i  =  r  45' 
8  =  0.450 
D  =  0.450  X  200  =  90  lb. 

In  the  case  of  the  biplane  -^  is  seen  to  be  8  per  cent,  smaller 

than  in  the  case  of  the  monoplane.  The  thrust  required  is 
8  per  cent,  greater,  therefore  8  per  cent,  more  H.P.  is  re- 
quired to  move  the  wing  surfaces  of  this  biplane  than  that 
necessary  to  move  a  similar  wing  in  the  monoplane  structure. 
However,  the  final  deduction  must  not  be  made  that  a  bi- 
plane requires  8  per  cent,  more  power  than  the  monoplane 
of  equal  area.  The  power  absorbed  by  the  wing  system  is 
really  only  about  25  per  cent,  of  the  total  H.P.  required  by 
the  machine,  so  that  the  total  loss  due  to  the  employment 
of  a  biplane  structure  is  8  per  cent,  of  25  per  cent.,  or  2 
per  cent. 

Of  late,  the  biplane  structure  has  almost  entirely  sup- 
planted that  of  the  monoplane,  due  largely  to  the  great 
superiority,  from  a  structural  point  of  view,  offered 
by  a  cellular  structure  over  a  linear  type.  For  lifting 
surfaces  of  equal  areas,  the  biplane  takes  up  much  less  ground 
space  and  is  much  lighter  than  the  monoplane.     Regarding 

the  former,  the  pr — ^  ratio  being  the  same,  the  span  of 

the  biplane  is  only  0.71  that  required  by  the  monoplane. 

As  to  weight,  it  is  to  be  noted  that  a  wing  structure 
usually  consists  of  two  or  more  main  beams  called  wing 
spars,  running  parallel  to  the  span.  Wing  ribs,  constructed 
to  form  the  outline  of  the  wing  section,  are  fitted  to  the 
spars.  The  junction  of  the  wings  to  the  body  or  fuselage 
of  a  machine  is  made  by  means  of  the  spars,  which  are 
the  main  stress-resisting  members  of  the  wing.  The 
spars  of  monoplane  wings  are  fixed  or  hinged  to  the 
fuselage  and  braced  by  steel  cable  rigging  (Fig.  16).  In  the 
biplane,  instead,  the  corresponding  spars  of  both  upper  and 


16 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


lower  planes  are  held  together  by  struts  and  cross  bracing, 
forming  a  truss  (Fig.  17). 

For  those  familiar  with  the  principles  of  structures  it  is 
easy  to  see  the  great  superiority  of  the  biplane  structure 
over  the  monoplane  structure  in  stiffness  and  lightness, 
and  the  impossibility  of  monoplane  structure  in  large 
machines  because  of  its  excessive  weight. 


Fig.   1G. 

Wing  structure  is  becoming  more  and  more  uniform  for 
all  types  of  airplanes.  As  already  pointed  out,  the  frame 
consists  of  two  or  more  spars  on  which  the  ribs  are  fitted 
(Fig.  18).  A  leading  edge  made  of  wood  connects  the  front 
extremities  of  the  ribs,  while  for  the  trailing  edge  a  steel 
wire  or  wood  strip  is  used.  The  spars  are  also  held  together 
by  wooden  or  steel  tube  struts  and  steel  wire  cross  bracing, 


the  function  of  which  is  to  stiffen  the  wing  horizontally. 
The  rib  is  usually  built  up  with  a  thin  veneer  web,  to  which 
strengthening  flanges  are  glued  and  nailed  or  screwed 
(Fig.  19).  The  spars  are  usually  of  an  I,  channel,  or  box 
section  for  lightness  (Fig.  20). 

The  vertical  struts  between  the  upper  and  lower  wings 
of  a  biplane  may  be  either  of  wood  or  steel  tubing  (Fig.  21). 


THE  WINGS 


17 


In  either  case,  they  must  have  a  streamHne  section  in  order 
to  reduce  to  a  minimum  their  head  resistance.  Wood 
struts    are    often    hollowed    to    obtain    lightness.     Many 


,' In+vrmedia-te  Rihs  i-o  insure  a  good  Curva+ure 
•for  the  Leading Bdge. 


^  Forward  Spar. 


Angle  Slru-h 

BoxSecf/on--"^ 
End  Rib. 
EndFrH-mg-for 

to  the  Fuselage-''      ^ 
In+ermedialv 
"V'Sed-ion  Pib... 


ngTip 


Interior 
yfing  Trussing  Strut 


Rear  Spar 


Fig.  is. 


Interior  Sleel  tVire  Cross  SraC'nc 


SECTION    A-D 

(ENLARGED) 


Fig.  19. 
I 


Fig.  20. 


different  systems  of  connecting  the  struts  and  cables  to 
the  spars  are  used,  and  some  of  the  many  possible  methods 
are  shown  in  Fig.  22. 

The  wing  skeleton  is  covered  with  linen  fabric,  attached 
by  sewing  it  to  the  ribs,  and  tacking  or  sewing  it  to  the 


18 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


leading  and  trailing  edges.     It  is  then  given  an  application 


of  spec 
makes 


al  varnish,  called  ''dope,"  which  stretches  it  and 
t  air  tight.     The  surface  is  then  finished  with  bright 


-B(ENLAR6ECi) 


Fig.  21. 


Fig.  22. 


waterproof  varnish,  which  leaves  the  fabric  smooth  so  as 
to  reduce  frictional  losses  to  a  minimum,  thereby  detract- 
ing as  little  as  possible  from  the  efficiency. 


CHAPTER  II 
THE  CONTROL  SURFACES 

In  studying  the  directional  maneuvers  of  an  airplane, 
reference  must  be  made  to  its  center  of  gravity  (C.G.)  and  to 
its  three  principal  axes.  Two  of  the  axes  are  contained  in 
the  plane  of  symmetry  of  the  machine  while  the  third  is 
normal  to  this  plane.  One  of  the  two  axes  in  the  plane  is 
parallel  to  the  line  of  flight  while  the  other  is  perpendicular 
to  it. 

By  a  known  principle  of  mechanics,  every  rotation  of  the 
machine  about  its  C.G.  may  be  considered  as  the  resultant 
of  three  distinct  rotations,  one  about  each  of  the  three 
principal  axes.  On  the  other  hand,  if  three  systems  of 
control  are  used,  each  capable  of  producing  a  rotation  of 
the  airplane  about  one  of  its  principal  axes,  any  rotation 
of  the  machine  about  its  C.G.  can  be  brought  about  or 
prevented. 

The  principal  axis  perpendicular  to  the  plane  of  sym- 
metry, is  called  the  pitching  axis.  Rotations  about  that 
axis  are  called  pitching  movements.  The  devices  used  to 
bring  about,  or  prevent  a  pitching  movement  are  called 
devices  of  longitudinal  stability. 

The  axis  perpendicular  to  the  line  of  flight,  in  the  plane 
of  symmetry  is  called  the  axis  of  direction  of  flight.  The 
devices  which  cause  or  prevent  movements  about  that  axis 
are  called  devices  of  directional  stability. 

The  axis  parallel  to  the  line  of  flight  is  called  the  rolling 
axis,  and  the  devices  causing  or  preventing  rolling  move- 
ments are  called  devices  of  lateral  stabilit3^ 

There  are  usually  two  surfaces  which  control  longitudinal 
stability,  one  fixed,  called  the  stabilizer  or  tail  plane,  and 
the  other  movable,  called  the  elevator. 

The  stabilizer  or  tail  plane  is  a  relatively  small  surface 
fixed  at  the  rear  end  of  the  fuselage.     Its  function  is,  first 

19 


20  AIRPLANE  DESIGN  AND  CONSTRUCTION 

of  all,  to  offset  or  even  completely  invert  the  phenomenon 
of  the  inherent  instability  of  curved  wings,  and  secondly, 
to  act  as  a  damper  on  longitudinal  or  pitching  movements. 

The  stabilizer  may  be  of  various  shapes  and  sections. 
It  may  be  either  lifting  or  non-lifting,  but  it  must  always 
satisfy  the  basic  condition  that  its  unit  loading  per  sq.  ft. 
be  lower  than  that  of  the  principal  wing  surface.  Under 
this  condition  only,  will  it  act  as  a  stabilizer;  otherwise  it 
would  add  to  the  instability  of  the  wings. 

As  to  the  proper  dimensions  of  the  stabilizer,  they  depend 
on  various  factors  such  as  the  weight  of  the  airplane,  its 
longitudinal  moment  or  inertia,  its  speed,  and  the  distance 
the  stabilizer  is  set  from  the  center  of  gravity  of  the 
machine.  Moreover,  the  proportions  of  the  stabilizer  with 
respect  to  the  other  parts  of  the  airplane  are  also  dependent 
on  another  factor:  the  tj^pe  of  airplane.  For  small,  swift 
combat  machines  which  require  a  high  degree  of  maneuvera- 
bility, the  stabilizer  will  require  relatively  less  surface 
than  that  required  for  large,  heavily  loaded  machines,  such 
as  those  used  for  bombing  operations  and  requiring  a  much 
lower  degree  of  maneuverability. 

The  framework  or  skeleton  of  the  stabilizer  is  generally 
of  wood  or  steel  tubing.  In  general  its  angle  of  incidence 
may  be  adjusted  either  on  the  ground  or  while  in  flight. 
However,  that  incidence  must  never  be  greater  than  the 
angle  used  for  the  main  wing  surfaces.  Its  value  is  gen- 
erally 1°  to  4°  less  than  that  of  the  wings. 

The  elevator  or  movable  surface  is  hinged  to  the  rear 
edge  of  the  stabilizer,  and  it  may  be  raised  or  lowered 
while  in  flight. 

In  normal  flight  the  elevator  is  set  parallel  to  the  air 
flow  so  that  there  is  no  air  reaction  on  its  faces.  If  it  is 
swung  upward  or  downward  the  air  will  strike  it,  producing 
a  reaction  whose  direction  is  upward  or  downward  respec- 
tively, thus  tending  to  set  the  machine  for  climbing  or 
descending. 

The  size  of  the  elevator  also  depends  on  the  weight, 
moment  of  inertia,  speed  of  the  machine,  and  on  its  dis- 


THE  CONTROL  SURFACES 


21 


tance  from  the  center  of  gravity  of  the  machine;  also  the 
type  of  airplane  and  the  service  for  which  it  is  intended  must 
be  given  consideration.  However,  for  quick  and  responsive 
machines  the  elevator  must  be  proportionally  larger  than 


Fig.  23. 


for  slow  machines  endowed  with  a  greater  degree  of  stabil- 
ity. In  other  words,  the  two  proportions  vary  inversely 
as  those  of  the  stabiUzers.  However,  this  will  be 
more  easily  understood  upon  considering  the  functions  of 


22  AIRPLANE  DESIGN  AND  CONSTRUCTION 

the  two  devices  which  are  in  a  certain  sense,  completely 
opposite. 

The  function  of  the  stabilizer  is  to  insure  longitudinal 
stability,  just  as  its  name  implies.  The  elevators  function 
instead,  is  to  disturb  the  equilibrium  of  the  machine  in 
order  to  bring  about  a  change  in  the  normal  flying.  An 
outline  of  a  type  of  stabiUzer  and  elevator  system  is 
given  in  Fig.  23. 

A  closer  study  may  now  be  made  of  the  function  of  these 
two  parts  of  longitudinal  stability.  First  of  all,  examina- 
tion will  be  made  of  the  mechanism  by  which  the  stabilizer, 
when  properly  set,  exercises  its  stabilizing  property. 

When,  in  an  airplane,  the  incidence  of  the  wing  is  changed 
with  respect  to  the  air,  through  which  it  is  progressing,  the 
air  reaction  will  not  only  vary  in  intensity  but  also  in  loca- 
tion. If  the  new  reaction  is  such  as  to  antagonize  the 
deviation,  the  airplane  is  said  to  be  stable;  otherwise  it  is 
said  to  be  unstable. 

Wings  having  curved  profiles,  when  acting  alone,  are  un- 
stable. Laboratory  experiments  have  shown  that  for  a 
wing  with  a  curved  profile,  the  reaction  moves  forward  as 
the  incidence  is  increased,  and  vice  versa;  thus  the  reaction 
moves  in  such  a  way  as  to  aggravate  the  disturbance.  The 
point  of  intersection  of  the  air  reaction  on  the  wing  chord  is 
called  the  center  of  pressure  of  the  wing  (Fig.  24) .  The 
location  of  the  center  of  pressure  is  usually  indicated  by  the 

ratio  -•     The  curves  for  X  and  for      as  functions  of  the 
c  c 

angle  of  incidence  for  a  given  wing  section,  are  shown  in 

Fig.  25.    By  applying  the  data  from  these  curves  to  a  wing  of 

5  ft.  chord  and  40  ft.  span,  supposing  the  normal  speed  to 

be  100  m.p.h.  and  the  normal  angle  of  flight  2°,  the  wing 

loading  will  be 

L  =  7.5  X  200  =  1500  lb. 

and  it  will  be  in  equilibrium  if  the  center  of  gravity  of  the 
load  falls  at  a  distance  of  40  per  cent,  of  the  chord,  or  2 
ft.  from  the  leading  edge.     Suppose  now  that  the  inci- 


THE  CONTROL  SURFACES 


23 


dence  is  increased  from  2°  to  4°,  then  the  sustaining  force 
becomes 

L  =  10  X  200  -  2000  lb. 


17.5 


15.0 


12.5 


10.0 


7.5 


5.0 


2.5 


> 

/ 

I  - 

*  ■>  ^               *c                                 > 

^  v^                   ■»                                                                ^ 

■''^          •"                                                          / 

1         ^  w                                                      ^ 

'    ^^s                        y^ 

'^s                    /'^ 

^s         / 

"^^ 

- ^Z   ^k_ 

tL           ^^ 

^^                                   ^-' 

/                                                    ^^^^ 

^^ 

7 

^  /^ 

-?/ 

/ 

^'^ 

7 

y 

/ 

/        -                                                           ( 

\j 

/ 

A- 

2C. 

c 

0.50 


0.45 


0.40 


0.35 


0.30 


0.25 


0.20 


0.15 


-3-2-10        1234567       69 
Degrees. 
Fig.  25. 

and  it  will  be  applied  at  37  per  cent,  of  the  chord,  or  1.85 
ft.  from  the  leading  edge;  this  result  will  then  produce 
around  the  center  of  gravity,  a  moment  of 

2000  X  0.15  =  300  ft.  lb. 


24  AIRPLANE  DESIGN  AND  CONSTRUCTION 

and  such  moment  will  tend  to  make  the  machine  nose  up; 
that  is,  it  will  tend  to  further  increase  the  angle  of  inci- 
dence of  the  wing.  Following  the  same  line  of  reasoning  for 
a  case  of  decrease  in  the  angle  of  incidence,  it  will  be  found 
in  that  case  that  a  moment  is  originated  tending  to  make  the 
machine  nose  down.  Therefore,  the  wing  in  question  is 
unstable. 

A  practical  case  will  now  be  considered,  where  a  stabil- 
izer is  set  behind  this  wing,  and  constituted  of  a  surface  of 
15  sq.  ft.  (2  X  7.5)  set  in  such  a  manner  as  to  present  an 
angle  of  —2°  with  the  line  of  flight  w-hen  the  wdng  in  front 
presents  an  angle  of  +  2°.     In  normal  flight  there  is 

1 .  The  sustaining  force  of  the  main  w  ing,  equal  to 

L,  =  7.5  X  200  =  1500  lb. 

2.  The  center  of  pressure  of  the  main  wing  located  at 

0.40  X  5  =  2  ft.  from  the  leading  edge, 

3.  The  sustaining  force  of  the  elevator  equal  to 

L,  =  2.3  X  15  =  33.5  lb.,  and 

4.  The  center  of  pressure  of  the  elevator  located  at 

0.44  X  2'  =  0.88  ft.  from  its  leading  edge. 
Suppose  now  that  the  incidence  of  the  machine  is  in- 
creased so  that  the  angle  of  incidence  of  the  front  wing 
changes  from  +2°  to  +5°,  then  there  is 

1.  The  sustaining  force  of  the  main  wing  equal  to 

L,  =  11.30  X  200  =  2260  lb. 

2.  The  center  of  pressure  of  the  main  wing  located  at 

0.355  X  5'  =  1.78  ft., 

3.  The  sustaining  force  of  the  elevator  equal  to 

L,  =  6.05  X  15  =  91  lb.,  and 

4.  The  center  of  pressure  of  the  elevator  located  at 

0.410  X  2'  =  0.82  ft.  from  its  leading  edge. 
With  these  values,  the  total  resultant  of  the  forces  acting 
in  each  case  is  obtained,  and  it  is  found  that  while  in  nor- 
mal flight,  the  moment  of  total  resultant  about  the  e.g.  of 
the  machine  is  equal  to  zero;  when  the  incidence  is  increased 

Library 
N.  C.  State   College 


THE  CONTROL  SURFACES 


25 


to  5°,  that  moment  becomes  equal  to  2351  X  (2.71'  -  2.50') 
=  493  ft.  lb.  tending  to  make  the  machine  nose  down; 
that  is,  tends  to  prevent  the  deviation  and  therefore  is  a 
stabilizing  moment  (Fig.  26). 

In  analogous  manner  it  can  be  shown  that  if  the  incidence 
of  the  machine  is  decreased,  a  moment  tending  to  prevent 


\J'l5Sq.Ff 


Ls'33.5/tS. 


iL^^9//t>s. 


Fig.  26. 


that  deviation  is  developed.  It  is  obvious,  then,  that  if 
the  airplane  were  provided  with  only  a  stabilizer  and  with 
no  elevator,  it  would  fly  at  only  one  certain  angle  of  inci- 
dence, since  any  change  in  this  angle  would  develop  a  stabil- 
izing moment  tending  to  restore  the  machine  to  its  original 
angle.  Thus  the  exact  function  of  the  elevator  is  to  pro- 
duce moments  which  will  balance  the  stabilizing  moments 


26 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


due  to  the  stabilizer.  This  will  allow  the  machine  to  assume 
a  complete  series  of  angles  of  incidence,  enabling  it  to 
maneuver  for  climbing  or  descending. 

There  are  also  usually  two  parts  controlling  directional 
stability;  one  fixed  surface  called  the  fin  or  vertical  stabilizer, 
and  one  movable  surface  called  the  rudder. 

Consider,  for  example,  an  airplane  in  normal  flight;  that 
is.  with  its  line  of  flight  coincident  with  the  rolling  axis 


(Fig.  27).  In  this  case  there  is  no  force  of  drift,  but  if 
for  some  reason  the  line  of  flight  is  no  longer  coincident 
with  the  rolling  axis,  a  force  of  drift  is  developed  (Fig.  28), 
whose  point  of  application  is  called  center  of  drift.  If 
this  center  is  found  to  lie  behind  the  center  of  gravity,  the 
machine  tends  to  set  itself  against  the  wind;  that  is,  it 
becomes  endowed  with  directional  stability.  If,  instead, 
the  center  of  drift  should  fall  before  the  center  of  gravity, 
normal  flight  would  be  impossible,  as  the  machine  tends  to 


THE  CONTROL  SURFACES 


27 


turn  sharply  about  at  the  least  deviation  from  its  normal 
course.  In  practice,  since  the  center  of  gravity  of  an  air- 
plane is  found  very  close  to  the  front  end  of  the  machine, 
the  condition  of  directional  stability  is  easily  attained  by 
the  use  of  a  small  vertical  surface  of  drift  which  is  set 
at  the  extreme  rear  of  the  fuselage.  This  surface  is  called 
the  fin  or  vertical  stabilizer. 

There  is,  however,  a  type  of  airplane  called  the  Canard 


Fig.  28. 


type,  in  which  the  main  wing  surface  is  the  one  in  the  rear, 
(and  consequently  the  e.g.  falls  entirely  in  the  rear)  and 
in  which  the  problem  of  directional  stability  presents 
considerable  difficulty.  This  type  of  airplane,  however,  is 
not  used  at  the  present  time. 

A  machine  provided  with  only  a  fin  would  possess  good 
directional  stability,  but  for  that  very  reason  it  would  be 
impossible  for  the  airplane  to  change  its  course.  For  that 
reason  it  is  necessary  to  have  a  rudder;  a  vertical  movable 


28 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


surface,  which,  when  properly  deviated,  will  produce  a 
balancing  moment  to  overcome  the  stabilizing  moment  of 
the  fin,  thus  permitting  a  change  in  the  course  of  the  drift. 
The  phenomenon  may  now  be  studied  more  in  detail. 
Let  us  suppose  that  the  directing  rudder  is  deviated  at  an 
angle;  this  deviation  will  then  provoke  on  the  rudder  a 
reaction  D'  (Fig.  29),  which  will  have  about  the  center  of 
gravity  a  moment  D'Xd';  as  a  result,  the  airplane  will 


Fig.  29. 


rotate  about  the  axis  of  direction  and  the  line  of  flight  will 
no  longer  coincide  with  the  rolling  axis;  that  is,  when  the 
airplane  starts  to  drift  in  its  course,  a  drifting  force  D"  is 
originated,  which  tends  to  stabilize,  and  when  D"  X  d"  = 
D'  X  d' ,  equilibrium  will  be  obtained.  Obviously,  then,  the 
line  of  flight  will  no  longer  be  rectiUnear,  since  the  two  forces 
D"  and  D'  are  unequal,  and  if  transported  to  the  center  of 
gravity  they  will  give  a  resultant  D  =  D"  —  D'  other  than 
zero.     The  equilibrium  will  be  obtained  only  if  the  line  of 


THE  CONTROL  SURFACES  29 

flight  becomes  curvilinear;  in  fact,  a  centrifugal  force  4>  is 
then  developed  which  will  be  in  equilibrium  with  the  re- 
sultant force  of  drift  D.  Then  equilibrium  will  be  obtained 
when  ^  =  D;  as 

W       V 
$  =  ^  X  — 
g  r 

where  W  is  the  weight  of  the  airplane,  g  the  acceleration  due 
to  gravity,  V  the  velocity  of  the  airplane  and  r  the  radius 
of  curvature  of  the  line  of  flight,  therefore 


a         r 


from  which  is  obtained 


W       V       W  V 


g  ^  D         g  ^  D"  -D' 

From  this  equation  it  will  be  seen  that  to  obtain  remarkable 
maneuverability  in  turning,  the  difference  D"  —  D'  must 
have  a  large  value.     Or,  since 

D'       d" 

it  is  necessary  that  the  center  of  drift,  although  being  in  the 
rear  of  the  center  of  gravity,  must  be  not  too  far  behind  it, 
and  it  is  necessary  that  the  rudder  be  located  at  a  consider- 
able distance  from  the  center  of  gravity.  In  other  words, 
for  good  maneuverability,  an  excessive  directional  stability 
must  not  exist.  The  foregoing  applies  to  what  is  called  a 
flat  turn  without  banking,  which  is  analogous  to  that  of  a 
ship.  The  airplane,  however,  offers  the  great  advantage  of 
being  able  to  incline  itself  laterally  which  greatly  facilitates 
turning,  as  will  be  shown  when  reference  is  made  to  the 
devices  for  transversal  stability. 

In  summarizing  the  foregoing,  it  is  seen  that  in  addition 
to  the  fixed  surfaces,  stabilizer  and  fin,  whose  functions  are 
to  insure  longitudinal  and  directional  stability,  airplanes 
are  provided  with  movable  surfaces,  elevator  and  rudder, 
which  are  intended  to  produce  moments  to  oppose  the 
stabilizing  moments  of  the  fixed  devices.     It  will  now  be 


30  AIRPLANE  DESIGN  AND  CONSTRUCTION 

better  understood  that  excessive  stability  is  contrary  to 
good  maneuverability. 

In  like  manner,  for  transversal  stability,  there  are  two 
classes  of  devices  opposite  in  their  functions.  Some  are 
used  to  insure  stability  while  others  serve  to  produce 
moments  capable  of  neutralizing  the  stabilizing  moments. 

Let  us  consider  an  airplane  in  normal  flight,  and  suppose 
that  a  gust  of  wind  causes  the  machine  to  become  inclined 
laterally  by  an  angle  a.  The  weight  W  and  the  air  reaction 
L  will  have  a  resultant  D„  which  will  tend  to  make  the 


f 

V 

r 

\ 

.,__- 

^ 

b4 

1 

::>^ 

w 

Fio. 

30. 

machine  drift  (Fig.  30) ;  this  drifting  movement  will  produce 
a  lateral  air  reaction  —  Z>„  acting  in  the  direction  opposite 
to  Z)„.  The  resultant  of  the  lateral  wind  forces  acting  on 
the  machine  is  —  Z)„.  If  this  reaction  is  such  as  to  make 
with  the  force  D^  a  couple  tending  to  restore  the  machine 
to  its  original  position,  the  machine  is  said  to  be  transver- 
sally  stable;  this  is  the  case  shown  in  Fig,  30.  If  —D„  has 
the  same  axis  as  Z)„,  the  au-plane  is  said  to  have  an  indif- 
ferent transversal  stability.  If,  finally,  —D^  and  D^  form 
a  couple  tending  to  aggravate  the  inclination  of  the  machine, 
the  latter  is  said  to  be  transversally  unstable. 

Consequently,  in  order  to  have  an  airplane  laterally 
stable,  conditions  must  be  such  that  the  lateral  reaction 
—  Z)„  together  with  the  force  D„  form  a  stabilizing  couple; 
that  is,  the  point  of  application  of  the  force  —  Z)„  must  be 


THE  CONTROL  SURFACES 


31 


situated  above  the  point  of  application  of  force  Z)„,  which  is 
the  center  of  gravity.  However,  the  couple  of  lateral 
stability  must  not  have  an  excessive  value,  as  it  would 
decrease  the  maneuverability  to  such  an  extent  as  to  make 
the  machine  dangerous  to  handle,  as  will  now  be  explained. 
It  has  been  explained  before  how  a  turning  action  may 
be  obtained  by  merely  maneuvering  the  rudder,  and  how 


^=-D^=Lsinoc  =  Wtanoc 


this  cannot  be  actually  done  in  practice  since  there  is  a 
possibility  of  the  machine  banking  while  turning.  Now, 
when  the  airplane  "banks,"  the  forces  L  and  W  will  admit 
a  lateral  resultant  D^  which  tends  to  deviate  laterally  the 
line  of  flight.  A  centrifugal  force  <i>  is  thereby  developed, 
tending  to  balance  the  force  Z)„  and  equilibrium  will  obtain 
when  <l>  =  Z)„  (Fig.  31);  that  is,  when 


32  AIRPLANE  DESIGN  AND  CONSTRUCTION 

where  r  is  the  radius  of  curvature  of   the  Hne  of  flight; 
therefore 


D„  -- 

W 

g 

r 

vhich 

will  give 

r  = 

w     v^ 
g^D~. 

isD„ 

=  IF  tan 

a, 

we  obt; 

ain 

r  = 

'x 

72 

tan 

This  equation  shows  that  the  turn  can  be  so  much  sharper 
as  the  speed  is  decreased,  and  the  angle  a  of  the  bank  is 
increased.  This  explains  why  pilots  desiring  to  turn 
sharply,  make  a  steep  bank  and  at  the  same  time  nose  the 
machine  upward  in  order  to  lose  speed. 

Now  the  angle  of  bank  may  be  obtained  in  two  ways;  by 
operating  the  rudder  or  by  using  the  ailerons  which  are 
the  controls  for  lateral  stability.  In  using  the  rudder, 
it  has  been  observed  that  the  machine  assumes  an  angle  of 
drift.  If  the  force  of  drift  D  =  D"  -  D'  (Fig.  29)  passes 
through  the  center  of  gravity,  a  flat  turn  without  banking 
will  result.  If  force  D  passes  below  the  center  of  gravity, 
the  airplane  will  incline  itself  so  as  to  produce  a  resultant 
Z)„  of  L  and  W,  in  a  direction  opposite  to  force  D.  Then 
the  total  force  of  drift  is  equal  to  Z)  —  D„.  This  case  is 
of  no  practical  interest,  since  it  corresponds  to  the  case 
of  lateral  instability,  which  is  to  be  avoided.  If,  instead, 
force  D  passes  above  the  center  of  gravity,  then  the  angle 
of  bank  a  is  such  that  D^  is  of  the  same  direction  as  D. 
Therefore,  the  total  force  of  drift  is  D  +  D„. 

Now  if  force  Z)„  had  its  point  of  application  too  far  above 
the  center  of  gravity,  the  result  would  be  that  with  a  slight 
movement  of  the  rudder,  a  strong  overturning  moment 
would  develop  which  would  give  the  machine  a  dangerous 
angle  of  bank.  Therefore  it  is  evident  that  an  excessive 
stabilizing  moment  must  be  avoided. 


THE  CONTROL  SURFACES 


33 


The  ailerons  are  two  small  movable  surfaces  located  at 
the  wing  ends  (Fig.  32) .  Let  us  now  observe  what  happens 
when  they  are  operated. 

The  ailerons  are  hinged  along  the  axes  AA'  and  BB', 
and  are  controlled  in  such  a  manner  that  when  one  swings 
upward  the  other  swings  downward.  With  this  inverse 
movement,  the  equity  of  the  sustaining  force  on  both  the 


FiQ.  32. 


right  and  left  wings,  is  broken.  Thus  a  couple  is  brought 
into  play  which  tends  to  rotate  the  machine  about  the  rolling 
axis.  Since  it  is  possible  to  operate  the  ailerons  in  either 
direction,  the  pilot  can  bank  his  machine  to  the  right  or 
to  the  left. 

Supposing  that  the  pilot  operates  the  ailerons  so  that  the 
machine  banks  to  the  right;  let  a  be  the  angle  of  bank; 
then,  a  force  D^  is  produced,  which,  in  a  laterally  stable 
machine  will  tend  to  oppose  the  banking  movement  caused 


34 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


by  the  ailerons.  The  rapidity  of  turning,  and  consequently 
the  mobility  of  the  machine,  will  increase  in  proportion  as 
the  rapidity  of  the  banking  movement  increases.  Now,  all 
other  conditions  being  similar,  the  rapidity  with  which  the 
machine  banks  is  proportional  to  the  difference  of  the  couple 
due  to  the  actions  of  the  ailerons,  and  the  couple  due  to  the 
force  of  drift  a;  if  the  value  of  the  latter  is  very  large  (that 


Fig.  33. 

is,  if  D„  is  applied  very  far  above  the  center  of  gravity) 
the  maneuver  will  be  slow.  Therefore  for  good  mobility 
of  the  airplane,  the  force  Z)„  must  not  be  too  far  above 
the  center  of  gravity. 

The  foregoing  considerations  show  the  close  interdepend- 
ency  existing  between  the  problems  of  directional  stability 
and  those  of  transversal  stability.     It  is  practically  possible 


Fig.  34. 


to  control  directional  stability  by  means  of  the  lateral  con- 
trols, and  vice  versa.  For  example,  birds  possess  no  means 
of  control  for  directional  stability  alone,  but  use  the  motion 
of  their  wings  for  changing  the  direction  of  their  flight. 

To  raise  the  force  Z)„  with  respect  to  the  center  of  gravity, 
we  may  either  install  fins  above  the  rolling  axis,  or,  better 
still,  give  the  wings  an  upward  inclination  from  the  center 


THE  CONTROL  SURFACES 


35 


to  the  tip  of  the  wing,  the  so-called  dihedral  angle  (Fig.  33). 
The  effect  of  this  regulation  is  that  when  the  machine  takes  an 
angle  of  drift,  the  wing  on  the  side  toward  which  the  machine 
drifts,  assumes  an  angle  of  incidence  greater  than  the  inci- 


dence of  the  opposite  wing,  thereby  developing  a  lateral 
couple  which  is  favorable  to  stability. 

The  framework  of  the  ailerons  is  usually  of  wood,  steel 
tubing  or  pressed  steel  members.  An  outline  of  wood  ailer- 
ons is  given  in  Fig.  34. 

|3i 


Concluding,  to  be  relatively  safe  and  controllable  at  the 
same  time,  an  airplane  must  be  provided  with  devices  which 
will  produce  stabilizing  couples  for  every  deviation  from 
the  position  of  equilibriimi:  but  these  couples  must  not  be 


36 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


of  excessive  magnitude,  for  the  machine  would  then  be 
too  slow  in  its  maneuvers,  and  consequently  dangerous  in 
many  cases.  These  stabilizing  couples  must  be  of  the 
same  magnitude  as  the  couples  which  can  be  produced  by 
the  controlling  devices.  In  this  manner  the  pilot  always 
has  control  of  the  machine  and  it  will  answer  readily  and 
effectively  to  his  will. 

The  control  system  of  maneuvering  by  the  pilot  usu- 
ally consists  of  a  rudder-bar  operated  by  the  feet,  and  a 
hand-controlled  vertical  stick  (called  the  ''joy  stick")  piv- 


UNBM,ANCED  RUDDER 


BALANCED    RUDDER 
I  A' 


Fig.  37. 


oted  on  a  universal  joint,  moved  forward  and  backward  to 
lower  and  raise  the  elevator,  and  from  left  to  right  to  move 
the  ailerons  (Figs.  35  and  36). 

Balanced  rudders  are  found  on  some  of  the  high-powered 
machines,  as  they  reduce,  to  a  slight  degree,  the  muscular 
effort  of  the  pilot.  The  effort  required  to  move  a  control 
surface  depends  on  the  distance  h  (Fig.  37)  between  the 
center  of  pressure  C  and  the  axis  AB  of  rotation.  If  axis 
AB  is  moved  to  A'B',  the  value  of  h  is  reduced  to  h',  and 
therefore  the  required  effort  for  the  maneuver  is  decreased. 


CHAPTER  III 
THE  FUSELAGE 

The  fuselage  or  body  of  an  airplane  is  the  structure  usu- 
ally containing  the  engine,  fuel  tanks,  crew  and  the  useful 
load.  The  wings,  landing  gear,  rudder  and  elevator  are  all 
attached  to  the  fuselage.  The  fuselage  may  assume  any 
one  of  various  shapes,  depending  on  the  service  for  which 
the  machine  is  designed,  the  type  of  engine,  the  load,  etc. 
In  general,  however,  the  fuselage  must  be  designed  so  as 
to  have,  as  nearly  as  possible,  the  shape  of  a  solid  offering 
a  minimum  head  resistance.  In  the  discussion  on  wings, 
it  was  observed  that  the  air  reaction  acting  on  them  is  gen- 
erally considered  in  its  two  components  of  Lift  and  Drag. 
For  a  fuselage  moving  along  a  path  parallel  to  its  axis,  the 
Lift  component  is  zero,  or  nearly  so;  the  Drag  component 
is  predominant,  and  must  be  reduced  to  a  minimum  in 
order  to  minimize  the  power  necessary  to  move  the  fuselage 
through  the  air. 

Let  S  indicate  the  major  section  of  the  fuselage,  and  V 
the  velocity  of  the  airplane.  Laboratory  experiments  have 
shown  that  head  resistance  is  proportional  to  S  and  V^. 
Assuming  our  base  speed  as  100  m.p.h.  for  a  given  fuselage, 
then 

R-^  KXSX  (^f  (1) 

therefore,  if  >S  =  1  and  F  =  100,  then  R  ^  K.  Thus  the 
coefficient  A'  is  the  head  resistance  per  square  foot  of  the 
major  section  of  the  fuselage,  when  V  =  100  m.p.h.  This 
is  called  the  coefficient  of  penetration  of  the  fuselage.  The 
lower  K  is,  the  more  suitable  will  be  the  fuselage,  as  the 
corresponding  necessary  power  will  be  decreased. 

Equation  (1)  shows  two  ways  of  decreasing  the  necessary 
power; 

(a)  By  reducing  the  major  section  of  the  fuselage  to  a 

minimum,  and  (6)  by  lowering  the  value  of  coefficient  K  as 

much  as  possible. 

37 


38 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


In  order  to  solve  problem  (a)  it  is  necessary  first  to  adapt 
the  section  of  the  fuselage  to  that  of  the  engine.     The 


Fr;.   38. 

fuselage  may  be  of  circular,  square,  rectangular,  triangular, 
etc.,  section,  so  designed  that  its  major  section  follows  the 
form  of  the  major  section  of  the  engine.  In 
the  second  place,  it  is  good  practice,  when  other 
reasons  do  not  prevent  it,  to  arrange  the  various 
masses  constituting  the  load  (fuel,  pilot,  pas- 
sengers, etc.)  one  behind  the  other,  so  as  to  keep 
the  transversal  dimension  as  small  as  possible. 

To  decrease  the  coefficient  of  head  resistance, 
the  shape  of  the  fuselage  must  be  carefully 
designed,  especially  the  form  of  the  bow  and  of 
the  stern.  Analogous  to  that  of  the  wings,  the 
phenomenon  of  head  resistance  of  the  fuselage 
is  due  to  the  resultant  of  two  positive  and 
negative  pressure  zones,  developing  on  the 
forward  and  rear  ends  respectively  (Fig.  38). 
Whatever  be  the  means  employed  to  reduce 
the  importance  of  those  zones,  the  value  of  K 
will  be  lowered,  thus  improving  the  penetration 
of  the  fuselage. 

To  improve  the  bow,  it  must  be  given  a  shape 
which  will  as  nearly  as  possible  approach  that  of 
the  nose  of  a  dirigible.  This  is  easily  affected 
with  engines  whose  contours  are  circular,  but 
the  problem  presents  greater  difficulties  with 
vertical  types  of  engines,  or  V  types  without 
reduction  gear.  Sometimes  a  bullet-nosed  cowling  is 
fitted  over  the  propeller  hub,  fixed  to  and  rotating  with 


Fig.  39. 


THE  FUSELAGE 


39 


the  propeller.  Its  form  is  then  continued  in  the  front  end 
of  the  fuselage  contour,  its  lines  gradually  easing  off  to 
meet  those  of  the  fuselage  (Fig,  39). 

To  improve  the  stern  of  the  fuselage  it  must  be  given  a 
strong  ratio  of  elongation,  and  the  shaping  with  the  rest  of 
the  machine  must  be  smoothly  accomplished.  A  special 
advantage  is  offered  by  the  reverse  curve  of  the  sides;  in 
fact,  in  this  case,  a  deviation  in  the  air  is  originated  in  the 
zone  of  reverse  curving  (Fig.  40)  tending  to  decrease  the 
pressure,  and  consequently  increasing  the  efficiency. 


Fig.   40 

The  value  of  coefficient  K  varies  from  7  (for  the  usual 
types  of  fuselage)  to  2.8  (for  perfect  dirigible  shapes).  It 
is  interesting  to  compare  such  values  with  the  coefficient 
of  head  resistance  of  a  flat  disc  1  sq.  ft.  in  area,  which  is 
equal  to  30.  To  move  the  above  disc  at  a  speed  of  100 
m.p.h.  we  must  overcome  a  resistance  of  30  lb.,  while  in  the 
case  of  the  fuselage  of  equal  section,  but  having  a  perfect 
streamline  shape,  we  must  overcome  a  resistance  of  only 
2.8  lb.,  or  less  than  one-tenth  the  head  resistance  of  the 
disc.  Practically,  a  well-shaped  fuselage  has  a  coefficient  of 
about  6,  so  if  its  major  section  is,  for  instance,  12  sq.  ft., 
the  resistance  to  be  overcome  at  a  speed  of  150  m.p.h.  is 

6  X  12  X  (J-^V  =  162  lbs. 

which  will  theoretically  absorb  about  66  H.P. 

Fuselages  may  be  divided  into  three  principal  classes, 
depending  on  the  type  of  construction  used: 

(a)  Truss  structure  type, 

(6)  Veneer  type,  and 

(c)  Monocoque  type. 


40  AIRPLANE  DESIGN  AND  CONSTRUCTION 


Mo+orSupporj-s. 
^ Motor  Supportinq  Beams. 


Tran&verse  Stru-h. 


Fig.  41. 


Veneer 

Panel 


Sfrffening  Wood  Cross-Bracing. 


^  Moior  Supports, 
Motor  Supportinj-Beams. 


Fig.  42. 


THE  FUSELAGE  41 

The  truss  type  generally  consists  of  4  longitudinal  longer- 
ons, held  together  by  means  of  small  vertical  and  horizontal 
struts  and  steel  wire  cross  bracing  (Fig.  41).  The  whole 
frame  is  covered  in  the  forward  part  with  veneer  and  alumi- 
num and  in  the  rear  with  fabric.  The  longerons  are  gen- 
erally of  wood,  and  the  small  struts  are  often  of  wood, 
although  sometimes  they  are  made  of  steel  tubing. 

Fuselages  built  of  veneer  are  similar  to  the  truss  type  as 
they  also  have  4  longitudinal  longerons,  but  the  latter, 
instead  of  being  assembled  with  struts  and  bracing,  are  held 
in  place  by  means  of  veneer  panels  glued  and  attached  by 
nails  or  screws.  By  the  use  of  veneer,  which  firmly  holds 
the  longerons  in  place  along  their  entire  length,  the  section 
of  the  longerons  can  be  reduced  (Fig.  42). 

The  monocoque  type  has  no  longerons,  the  fuselage 
being  formed  of  a  continuous  rigid  shell.  In  order  to  insure 
the  necessary  rigidity,  the  transverse  section  of  the  mono- 
coque is  either  circular  or  elliptical.  The  material  gener- 
ally used  for  this  type  is  wood  cut  into  very  thin  strips, 
glued  together  in  three  or  more  layers  so  that  the  grain  of 
one  ply  runs  in  a  different  direction  than  the  adjacent 
plies.  This  type  of  construction  has  not  come  into  general 
use  because  of  the  time  and  labor  required  in  comparison 
with  the  other  two  types,  although  it  is  highly  successful 
from  an  aerodynamical  point  of  view. 

Whatever  the  construction  of  the  fuselage  be,  the  distribu- 
tion of  the  component  parts  to  be  contained  in  it  does  not 
vary  substantially.  For  example,  in  a  two-seater  biplane 
(Fig.  43) ,  at  the  forward  end  we  find  the  engine  with  its  radia- 
tor and  propeller;  the  oil  tank  is  located  under  the  engine, 
and  directly  behind  the  engine  are  the  gasoline  tanks,  located 
in  a  position  corresponding  to  the  center  of  gravity  of  the 
machine.  It  is  important  that  the  tanks  be  so  located,  as 
the  fuel  is  a  load  which  is  consumed  during  flight,  and  if  it 
were  located  away  from  the  center  of  gravity,  the  constant 
decrease  in  its  weight  during  flight  would  disturb  the 
balance  of  the  machine. 


42  AIRPLANE  DESIGN  AND  CONSTRUCTION 


THE  FUSELAGE  43 

Directly  behind  the  tanks  is  the  pilot's  seat,  and  behind 
the  pilot  is  the  observer.  Fig.  43  shows  the  positions  of  the 
machine-guns,  cameras,  etc.  The  stabilizing  longitudinal 
surfaces  and  the  directional  surfaces  are  at  the  rear  end  of 
the  fuselage.  The  wings,  which  support  the  entire  weight 
of  the  fuselage  during  flight,  are  attached  to  that  part 
on  w^hich  the  center  of  gravity  of  the  machine  will  fall. 
Under  the  fuselage  is  placed  the  landing  gear.  Its  proper 
position  with  respect  to  the  center  of  gravity  of  the  machine 
will  be  dealt  with  later  on. 


CHAPTER  IV 
THE  LANDING  GEAR 

The  purpose  of  the  landing  gear  is  to  permit  the  airplane 
to  take  off  and  land  without  the  aid  of  special  launching 
apparatus. 

The  two  principal  types  of  landing  gears  are  the  land  and 
marine  types.  There  is  a  third,  which  might  be  called  the 
intermediate  type,  the  amphibious,  which  consists  of  both 
wheels  and  pontoons,  enabling  a  machine  to  land  or  ''take 


Fig.  44. 

off"  from  ground  or  water.  This  discussion  will  be  devoted 
solely  to  wheeled  landing  gears,  the  study  of  which  pertains 
especially  to  the  outlines  of  the  present  volume. 

The  ''take  off"  and  landing,  especially  the  latter,  are 
the  most  delicate  maneuvers  to  accomplish  in  flying. 
Even  though  a  large  and  perfectly  levelled  field  is  avail- 
able, the  pilot  when  landing  must  modify  the  line  of  flight 
until  it  is  tangent  to  the  ground  (Fig.  44) ;  only  by  doing 
this  will  the  kinetic  force  of  the  airplane  result  parallel  to 
the  ground,  and  only  then  will  there  be  no  vertical  com- 
ponents capable  of  producing  shocks. 

44 


THE  LANDING  GEAR 


45 


In  actual  practice,  however,  the  maneuvers  develop  in 
a  rather  different  manner.  First,  the  fields  are  never 
perfectly  level,  and  secondly,  the  line  of  flight  is  not  always 
exactly  parallel  to  the  ground  when  the  machine  comes  in 
contact  with  the  ground.  The  landing  gear  must  therefore 
be  equipped  with  shock  absorbers  capable  of  absorbing 
the  force  due  to  the  impact. 

The  system  of  forces  acting  on  an  airplane  in  flight  is 
generally  referred  to  its  center  of  gravity,  but  for  an  air- 


=  Tofal  Liffoffhe  Ylmga  and  Horizontal  Tail  Planes. 


T-  Propeller  Thrust.  ^ 


G=  Reaction  of  6round. 


Fig.  45. 


plane  moving  on  the  ground,  the  entire  system  of  the  acting 
forces  must  be  referred  to  the  axis  of  the  landing  wheels. 
Such  forces  are  (Fig.  45), 
T   =  propeller  thrust, 
W  =  weight  of  airplane, 
L    =  total  lift  of  wing  surfaces, 

=  total  head  resistance  of  airplane, 
=  inertia  force, 

=  friction  of  the  landing  wheels,  and 
=  reaction  of  the  ground. 
The  moments  of  these  forces  about  the  axis  of  the  landing 
gear  may  be  divided  into  four  groups: 

1.  Forces  whose  moments  are  zero  (the  reaction  of  the 
ground,  G), 


46  AIRPLANE  DESIGN  AND  CONSTRUCTION 

2.  Forces  whose  moments  will  tend  to  make  the  machine 
sommersault  (forces  T  and  F), 

3.  Forces  whose  moments  tend  to  prevent  sommersault- 
ing  (forces  W  and  R),  and 

4.  Forces  whose  moments  may  aid  or  prevent  sommer- 
saulting  (forces  L  and  7) . 

In  group  4,  the  moment  of  the  force  L  may  be  changed 
in  direction  at  the  pilot's  will,  by  maneuvering  the  ele- 
vator; force  I  prevents  sommersaulting  when  the  machine 
accelerates  in  taking  off,  and  aids  sommersaulting  in 
landing  when  the  machine  retards  its  motion. 

In  practice  it  is  possible  to  vary  the  value  of  these  mo- 
ments by  changing  the  position  of  the  landing  gear,  placing 
it  forward  or  backw^ard. 

By  placing  the  landing  gear  forward,  the  moment  due  to 
the  weight  of  the  machine  is  particularly  increased,  and  it 
may  be  carried  to  a  limit  where  this  moment  becomes  so 
excessive  that  it  cannot  be  counterbalanced  by  moments 
of  opposite  sign.  Then  the  airplane  wdll  not  "take  off," 
for  it  cannot  put  itself  into  the  line  of  flight. 

By  placing  the  landing  gear  backward,  the  moment  due 
to  the  weight  is  decreased,  and  this  may  be  done  until  the 
moment  is  zero,  and  it  can  even  become  negative;  then  the 
machine  could  not  move  on  the  ground  without  sommer- 
saulting. Consequently  it  is  necessary  to  locate  the  land- 
ing gear  so  that  the  tendency  to  sommersault  will  be  de- 
creased and  the  "take  off "  be  not  too  difficult.  In  practice 
this  is  brought  about  by  having  an  angle  of  from  14°  to 
16°  between  the  line  joining  the  center  of  gravity  of  the 
machine  to  the  axis  of  the  wheels,  and  a  vertical  line  pass- 
ing through  the  center  of  gravity. 

Let  us  examine  the  stresses  to  which  a  landing  gear  is 
subjected  upon  touching  the  ground.  Assume,  in  this 
case,  an  abnormal  landing;  that  is,  a  landing  with  a  shock. 
(In  fact,  in  the  case  of  a  perfect  landing,  the  reaction  of  the 
ground  on  the  wheels  is  equal  to  the  difference  between 
the  weight  W  and  the  sustaining  force  L,  and  assumes  a 
maximum  value  when  L  =  0;  that  is,  when  the  machine  is 


THE  LANDING  GEAR  47 

standing.)  In  the  case  of  a  hard  shock,  due  either  to  the 
encounter  of  some  obstacle  on  the  ground,  or  to  the  fact 
that  the  Hne  of  flight  has  not  been  straightened  out,  the 
kinetic  energy  of  the  machine  must  be  considered.  That 
kinetic  energy  is  equal  to 

2       g 

where  g  is  the  acceleration  due  to  gravity,  and  V  the  velocity 
of  the  au'plane  with  respect  to  the  ground.  The  foregoing 
is  the  amount  of  kinetic  energy  stored  up  in  the  airplane. 

Naturally,  it  would  be  impossible  to  adopt  devices 
capable  of  absorbing  all  the  kinetic  energy  thus  developed, 
as  the  weight  of  such  devices  would  make  their  use  pro- 
hibitive. Experience  has  proven  that  it  is  sufficient  to  pro- 
vide shock  absorbers  capable  of  absorbing  from  0.5  per 
cent,  to  1  per  cent,  of  the  total  kinetic  energy.  Then  the 
maximum  kinetic  energy  to  be  absorbed  in  landing  an  air- 
plane of  weight  TT^  and  velocity  V,  is  equal  to 

W 
0.0025  to  0.0050  X  —  X  V^ 

g 

For  example,  for  an  airplane  weighing  2000  lb.,  moving  at 
a  velocity  of  100  m.p.h.  (146  ft.  per  sec),  assuming  0.004, 
it  will  be  necessary  that  the  landing  gear  be  capable  of 
absorbing  a  maximum  amount  of  energy  equal  to 

0.004  X  ^  X  146^  =  5300  ft  .-lb. 

The  parts  of  the  landing  gear  intended  to  absorb  the 
kinetic  energy  of  an  airplane  in  landing,  are  the  tires  and 
shock  absorbers.  Fig.  46  gives  the  work  diagrams  for  a 
wheel.  The  wheel  is  capable  of  absorbing  900  ft. -lb.  with  a 
deformation  of  0.25  ft.  Fig.  47  gives  the  diagram  of  the 
work  referred  to  per  cent,  elongation  for  a  certain  type  of 
elastic  cord.  The  work  absorbed  by  n  ft.  of  elastic  cord 
under  a  per  cent,  elongation  of  x  is  equal  to  the  product  er 

YPJTT  times  the  area  of  the  diagram  corresponding  to  x  per 


48 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


cent,  elongation.     Supposing,  for  instance,  to  have  a  shock  ab- 
sorbing system  32  ft.  long,  allowing  an  elongation  of  150  per 


8000 
7000 
6000 
5000 
tfj  4000 
3000 
2000 
1000 


~    .  -  -   -.     1  ,  1  1  - 

-        -     -  -        -  ---jjrft^ 

TZOO/b.A 

/     ' 

1  1 

:  _:   :        _  '^        j  '-     ±" 

t 

\/        I 

/t  J         |_ 

-T-    \/^X^tu.°i^-Ai^-A    ' 

41       i      411     ?i     ILLL        _j_ 

T'. 

^-- 

% 

:q:::: 

z± .  :            -  : 

0.5         010        0.15       0.20        025 
Fig.  46. 


cent. ;  the  work  that  it  can  absorb  is  equal  as  shown  in  the 
diagram  to  1800  ft.-lb.     As  this  gives  a  total  of  2700  ft.-U)., 


150 

~ 

~ 

~ 

~ 

~ 

~" 

~ 

~ 

~ 

~ 

~" 

"" 

~ 

~" 

— 

~ 

~ 

~ 

- 

~ 

r 

~ 

~ 

~ 

~ 

- 

~ 

~ 

~ 

no 
150 

110 
110 

■ 

^ 

" 

■* 

^ 

- 

~ 

"■ 

~ 

■ 

" 

■ 

■■ 

^ 

'°1 

^ 

' 

'' 

, 

/ 

70 
60 

50 

/ 

/ 

/ 

i 

so 

f 

/ 

/ 

0 

c 

^ 

' 

? 

° 

10< 

10 

5 

0 

07 

08 

09 

0 

IC 

0 

01 

0 

w 

1 

0 

«r 

2C 

0 

)02 

2 

a 

30 

3 

3 

0 

!03 

3E 

0 

D3( 

0 

« 

10* 

1" 

) 

Fig.  47. 


two  wheels  and  two  shock  absorbers  of  such  type  will  be 
sufficient  for  the  airplane  in  question. 


THE  LANDING  GEAR 


49 


Rubber  cord  shock  absorbers,  which  perform  work  by 
their  elongation,  have  proven  to  be  the  lightest  and  most 


Fig.  49. 


Fig.  50. 


practical.     Experiments  have  been  made  with  other  types, 
such  as  the  steel  spring,  hydraulic  and  pneumatic,  but  the 


50  AIRPLANE  DESIGN  AND  CONSTRUCTION 

results  have  shown  these  types  to  possess  but  Uttle  merit. 
Fig.  48  illustrates  an  example  of  elastic  cord  binding.  Fig. 
49  shows  the  outline  of  a  landing  gear. 

Up  to  this  point,  our  discussion  has  been  only  on  the 
vertical  component  of  the  kinetic  energy.  Consideration 
must  also  be  given  the  horizontal  component,  whose  only 
effect  is  to  make  the  machine  run  on  the  ground  for  a  cer- 
tain distance.  \Mien  the  available  landing  space  is  limited, 
the  machine  must  be  slowed  down  by  means  of  some  brak- 
ing device,  in  order  to  shorten  the  distance  the  machine 
has  to  roll  on  the  ground.  Friction  on  the  wheels,  head 
resistance  and  the  drag  all  have  a  braking  effect,  but  it 
often  happens  that  these  retarding  forces  are  not  sufficient. 
The  practice  therefore  prevails  of  providing  the  tail  skid 
with  a  hook,  which,  as  it  digs  into  the  ground,  exerts  on 
the  machine  an  energetic  braking  action  (Fig.  50).  On 
some  machines,  a  short  arm,  with  a  small  plow  blade  at  its 
lower  end,  is  attached  to  the  middle  of  the  landing  gear 
axle,  which  can  be  caused  to  dig  into  the  ground  and  pro- 
duce a  braking  effect. 

Similar  to  the  landing  gear,  the  tail  skid  is  also  provided 
with  a  small  elastic  cord  shock  absorber  to  absorb  the  kinetic 
energy  of  the  shock. 

On  certain  airplanes,  use  is  made  of  aerodynamical  brakes 
consisting  of  special  surfaces  which  normally  are  set  in  the 
line  of  flight,  and  consequently  offering  no  passive  resist- 
ances, but  when  landing  they  can  be  maneuvered  so  as  to 
be  disposed  perpendicularly  to  the  line  of  motion,  producing 
an  energetic  braking  force. 


CHAPTER  V 
THE  ENGINE 

The  engine  will  be  dealt  with  only  from  the  airplane 
designers  point  of  view.  For  all  the  problems  peculiar  to 
the  technique  of  the  subject,  special  texts  can  be  referred  to. 

There  are  various  types  of  aviation  engines — with  rotary 
or  fixed  cylinders,  air  cooled  or  water  cooled,  and  of  ver- 
tical, V,  and  radial  types  of  cylinder  disposition.  Whatever 
the  type  under  consideration,  there  exist  certain  funda- 
mental characteristics  which  enable  one  to  judge  the  engine 
from  the  point  of  view  of  its  use  on  the  airplane.  Such 
characteristics  may  be  grouped  as  follows: 

1.  Weight  of  engine  per  horsepower, 

2.  Oil  and  gasoline  consumption  per  horsepower  per  hour, 

3.  Ratio  between  the  major  section  of  the  engine  and  the 
number  of  horsepower  developed, 

4.  Position  of  the  center  of  gravity  of  the  engine  with 
respect  to  the  propeller  axis,  and 

5.  Number  of  revolutions  per  minute  of  the  propeller 
shaft. 

In  order  to  judge  the  light  weight  of  an  engine,  it  is  not 
sufficient  to  know  only  its  weight  and  horsepower;  it  is 
also  essential  to  know  it  specific  fuel  consumption.  If  we 
call  E  the  weight  of  the  engine,  P  its  power,  C  the  total 
fuel  consumption  per  hour  (gasoline  and  oil),  and  x  the 
number  of  hours  of  flight  required  of  the  airplane,  then  the 
smaller  the  value  of  the  following  equation,  the  lighter  will 
be  the  motor: 

y  =  P  +  X  X  p  (1) 

For  a  given  engine,  equation  (1)  gives  the  linear  relation 
between  y  and  x,  which  can  be  translated  into  a  simple, 

51 


52 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


graphic,  representation.     Let  us  consider  two  engines,  A 
and  B,  having  the  following  characteristics: 


Table  1 

Engine 

E 
lbs. 

r 

H.P. 

'4 

lbs.  per  H.P. 

c 

Iba. 

1 
lbs.  per  H.P. 

A 
B 

600 
750 

300 
300 

2 
2.5 

180 
144 

1 

0.6 
0.48 

For  engine  A,  equation  (1)  will  give  7/  =  2  +  0.6a-. 
For  engine  B,  equation  (1)  will  give  y  =  2.5  +  0.48x. 


y 

X 

.r^ 
^ 

\^~ 

A 

e^ 

-r^ 

A 

^ 

y 

y 

01        23456789       10 
;x  Hours 

Fig.  51. 

Translating  these  equations  into  diagrams  (Fig.  51),  we 
see  that  engine  A  is  lighter  than  engine  B,  for  flights  up  to 
4  hours  10  minutes  beyond  which  point,  B  is  the  lighter. 

If  a;  =  10  hours, 

then 

y.  =  8  lb. 
y.  =  7.3 

that  is,  B  has  an  advantage  of  0.7  lb.  per  H.P. ;  since  P  = 
300  H.P.  the  total  advantage  is  270  lb. 


THE  ENGINE  53 

Practically,  for  engines  of  the  same  general  types,  the 

C 
value  of  the  specific  consumption  c  =  p>  varies  around  the 

same  values.     In  that  case,  only  the  weight  per  horsepower, 

e  =  p  is  of  interest.     In  fact,  that  ratio  is  so  important  that 

it  may  often  be  convenient  to  adopt  an  engine  of  lower 

power  in  comparison  with  another  of  high  power,  for  the 

sole  reason  that  for  the  latter  the  above  ratio  is  higher. 

Let  us  suppose  that  we  wish  to  build  an  airplane  of  given 

horizontal  and  climbing  speed  characteristics,  capable  of 

carrying  fuel  for  a  flight  of  three  hours  and  a  useful  load  of 

600  lb.  (pilot,  observer,  arms,  ammunition,  devices,  etc.). 

Fixing  the  flying  characteristics  is  equivalent  to  fixing  the 

maximum  weight  per  horsepower,  of  the  machine  with  its 

complete  load.     In  fact,  we  shall  see  further  on  in  discussing 

W 
the  efficiency  of  the  airplane,  that  the  lower  the  ratio  p- 

between  the  total  weight  W,  and  the  power  P  of  the  motor, 
the  better  will  be  the  flying  characteristics  of  the  machine. 

W 

Supposing  for  example,  that  -p  =  10  lb.     Analyzing  the 

weight  W,  we  find  it  to  be  the  sum  of  the  following 
components : 

TF^  =  weight    of   airplane   without    engine   group 

and  accessories, 
Wp  =  weight  of  the  complete  engine  group, 
Wc  =  weight  of  oil  and  gasoline, 
Wu  =  useful  load. 

We  can  then  write 

W  =  W^  +  Wp  +  Wc  +  Wu 

Generally  W^  =  %  W;  Wp  =  eP.  In  this  case  (assuming 
4  hours  of  flight)  Wc  =  4CP,  where  C  is  the  specific  con- 
sumption per  horsepower  which  can  be  assumed  to  be  equal 
to  0.55;  this  gives  Wq  =  2.2P;  furthermore  Wv  =  600  lb. 


54  AIRPLANE  DESIGN  AND  CONSTRUCTION 

We  shall  then  have 

W  =  }i  W  +  eP  +  2.2P  +  600 

W 
that  is,  since  -p  must  be  equal  to  10 

P  _       600 
4.46  -  e 
and  consequently 

W  =  ^^  — 

0.446  -  O.le 

In  Fig.  52  these  relations  have  been  translated  into  curves, 
and  it  is  seen  that  there  are  innumerable  couples  of  values 
e,  P,  which  satisfy  the  conditions  necessary  for  the  construc- 
tion of  the  airplane  under  consideration. 

Let  us  examine  the  extreme  values  f or  e  =  2  lb.  per  H.P. 
and  e  =  3  lb.  per  H.P.     We  see  that 

if  e  =  2;  P  =  246  H.P.  and  W  =  2460  lb. 
if  e  =  3;  P  =  416  H.P.  and  W  =  4160  lb. 

From  these  it  is  obvious  then,  that  although  using  an 
engine  of  70  per  cent,  more  power,  the  same  result  is  ob- 
tained, plus  the  disadvantage  of  having  an  airplane  whose 
surface  (and  consequently  the  required  floor  space),  is 
70  per  cent,  greater. 

However,  in  practice  it  often  happens  that  an  engine  of 
higher  power  than  another,  not  only  does  not  possess  higher 
weight  per  horsepower,  but  on  the  contrary,  has  a  lower 
weight  per  horsepower.  It  is  only  necessary  to  note  the 
importance  of  this  matter. 

Another  important  consideration  is  the  bulk  of  the  en- 
gine. Of  two  engines  having  the  same  power,  but  different 
major  sections,  we  naturally  prefer  the  engine  of  lesser 
major  section,  because  it  permits  the  construction  of  fusel- 
ages offering  less  head  resistance.  An  example  will  make 
the  point  clearer.  Supposing  we  have  two  engines,  each 
of  300  H.P.,  whose  characteristics  with  the  exception  of 
their  bulk,  are  absolutely  similar.     Suppose  that  one  of 


THE  ENGINE 


55 


these  engines  has  a  major  section  of  6  sq.  ft.,  and  the  other 
of  9  sq.  ft.,  the  head  resistance  of  the  fuselage  of  the  second 
engine  is  50  per  cent,  greater  than  that  of  the  first.     Let 


400 

y 

y 

y 

\^ 

^    \ 

.^ 

y 

^ 

l^ 

300 

^ 

^ 

^ 

^ 

<-- 

^ 

"^ 

.-^ 

ZOO 

100 

e 

00 

4 

46- 

s 

. 

_J 

5000 


4000 


3000 


2000 


1000 


2.25 


2.50 


175 


us  assume  that  the  power  developed  is  used  up  in  the  fol- 
lowing   manner : 

30  per  cent,  for  the  resistance  of  the  wing  surface, 

40  per    cent,    for   the   resistance   of    the   fuselage,    and 

30  per  cent,  for  the  resistance  of  all  the  other  parts. 

The  result  is  that  with  the  second  engine,  a  machine  can  be 
constructed   whose  head  resistance   will   be  20  per  cent. 


56  AIRPLANE  DESIGN  AND  CONSTRUCTION 

greater,  thereby  losing  about  7  per  cent,  of  the  speed,  due  to 
the  relations  between  the  various  head  resistances  and  the 
speeds,  as  we  shall  see  in  the  discussion  on  the  efficiency  of 
the  airplane. 

The  position  of  the  center  of  gravity  with  respect  to 
the  propeller  axis,  has  a  great  importance  in  regard  to  the 
installation  of  an  engine  in  the  airplane.  An  ideal  engine 
should  have  its  center  of  gravity  below,  or  at  the  most,  coin- 
cident with  the  line  of  thrust.  This  last  condition  is  true 
for  all  rotary  and  radial  engines.  Instead,  for  engines  with 
vertical  or  V  types  of  cylinders,  the  center  of  gravity 
is  generally  found  above  the  line  of  thrust,  unless  the  pro- 
peller axis  is  raised  by  using  a  transmission  gear.  In 
speaking  of  the  problems  of  balancing,  we  shall  see  the  great 
importance  of  the  position  of  the  center  of  gravity  of  the 
machine  with  respect  to  the  axis  of  traction,  and  the  con- 
venience there  may  be  in  certain  cases,  of  employing  a  trans- 
mission gear  in  order  to  realize  more  favorable  conditions. 

Furthermore,  the  transmission  gear  from  the  engine  shaft 
to  the  propeller  shaft,  may  in  some  cases  prove  very  con- 
venient in  making  the  propeller  turn  at  a  speed  conducive 
to  good  efficiency.  In  the  following  chapter  we  shall  see 
that  the  propeller  efficiency  depends  on  the  ratio  between 
the  speed  of  the  airplane  and  the  peripheral  speed  of  the 
propeller;  since  the  peripheral  speed  depends  on  the  number 
of  revolutions,  this  factor  consequently  becomes  of  vast 
importance  for  the  efficiency.. 

Let  us  see  now  which  criterions  are  to  be  followed  in 
installing  an  engine  in  an  airplane,  and  let  us  discuss  briefly, 
the  principal  accessory  installations  such  as  the  gasoline 
and  oil  systems,  and  the  water  circulation  for  cooling. 

As  has  been  pointed  out  before,  in  the  type  of  machine 
most  generally  used  today,  the  tractor  biplane — the 
engine  is  installed  in  the  forward  end  of  the  fuselage — on 
properly  designed  supports,  usually  of  wood,  to  which  it 
is  firmly  bolted.  The  supports,  in  turn,  are  supported  on 
transverse  fuselage  bridging  and  are  anchored  with  steel 
wires  which  take  up  the  propeller  thrust  (Fig.  53). 


THE  ENGINE 


57 


58 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


The  oil  tank  is  generally  situated  under  the  engine,  so 
as  to  reduce  to  a  minimum  the  piping  system.  There 
are  two  pipe  lines — one  leading  from  the  bottom  of  the 
tank  and  which  is  used  for  the  suction,  the  other,  for  the 
return  and  leading  into  the  top  of  the  tank  (Fig.  54). 
The  oil  tank  is  usually  made  of  copper  or  leaded  steel  sheets; 
it  generally  weighs  from  10  per  cent,  to  12  per  cent,  as  much 
as  the  oil  it  contains. 

It  is  easy  to  place  all  the  oil  in  one  tank,  as  the  oil  con- 
sumption per  horsepower  is  about  ^{qq  of   the    gasoline 


Oil  Feed  and 
Refui'n  Pump 


-=-^        Return  Oil  Pump 


Filter 


Return  Pipe 


Fig.   54. 


consumption,  but  it  is  a  difficult  matter  to  contain  all  the 
required  gasoline  in  a  single  tank,  especially  for  powerful 
engines.  Therefore,  multiple  tanks  are  used.  As  the  gaso- 
line must  be  sent  to  the  carburetor  which  is  generally 
located  above  the  tanks,  it  is  necessary  to  resort  to  artifices 
to  insure  the  feeding.     The  principal  artifices  are 

a.  Air  pump  pressure  feed, 

h.  Gasoline  pump  feed. 

The  general  scheme  of  the  pressure  feed  is  shown  in  Fig. 
55.  The  motor  M,  carries  a  special  pump  P  which  compresses 
the  air  in  tank  T;  the  gasoline  flowing  through  cock  1, 
goes  to  carburetor  C  Cock  1  enables  the  opening  or  closing 
of  the  flow  between  tank  T  and  the  carburetor.     Further- 


THE  ENGINE 


59 


more,  it  allows  or  stops  a  flow  between  the  carburetor  and 
a  small  auxiliary  safety  tank  t,  situated  above  the  level  of 
the  carburetor,  so  that  the  gasoline  may  flow  to  the  carbu- 


FiG.  55. — Gasoline  pressure  feed  sj^stem. 

retor  by  gravity;  the  gasohne  in  this  tank  is  used  in  case 
the  feed  from  the  main  tank  should  cease  to  operate.     Fi- 


I     I     I     I     I     I 

pr^i     r^^   f^i     tTi     r]°i     f^    ^ 


Hei'ghi  of  Fall 

of  Gasoline 


nally,  cock  1  also  enables  a  flow  between  the  main  tank  T 
and  the  auxiliary  tank  t,  in  order  that  the  latter  may  be 
replenished.     The  scheme  of  circulation  is  completed  by  a 


60  AIRPLANE  DESIGN  AND  CONSTRUCTION 

hand  pump  p,  which  serves  to  produce  pressure  in  the  tank 
before  starting  the  engine;  cock  2  establishes  a  flow  between 
tank  T  and  either  or  both  of  the  pumps  P  and  p,  or  excludes 
them  both. 

Fig.  56  shows  the  scheme  of  circulation  by  using  the  gaso- 
line pump  feed.  The  gasoline  in  the  main  tank  T  flows  to 
a  pump  G,  which  sends  it  to  the  carburetor.  Cock  i 
permits  or  stops  a  flow  between  tank  T  and  the  carburetor, 
or  between  tank  t  and  the  carburetor,  or  between  T  and  /. 
Pump  G  may  be  operated  by  a  special  small  propeller  or 
by  the  engine. 

In  the  schemes  of  Figs.  55  and  56,  an  example  of  only 
one  main  tank  is  shown.  If  there  are  two  or  more  tanks 
the  conception  of  the  schemes  remains  the  same,  the  cocks 
only  changing  so  as  to  allow  simultaneous  or  single  func- 
tioning of  each  of  the  tanks. 

Gasoline  pump  feed  is  much  more  convenient  than  pres- 
sure feed  because  it  is  more  reliable.  It  does  not  use  com- 
pressed air,  is  less  tiresome  for  the  pilot,  as  it  requires  of 
him  only  the  maneuver  of  opening  or  closing  a  cock,  and 
finally,  because  the  tanks  can  be  much  lighter  as  they  do 
not  have  to  withstand  the  air  pressure. 

As  a  matter  of  interest,  a  tank  operating  under  pressure 
weighs  from  14  per  cent,  to  18  per  cent,  as  much  as  the 
gasoline  it  contains,  while  a  tank  operating  without  pres- 
sure weighs  from  10  per  cent,  to  13  per  cent. 

We  shall  note  finally,  that  it  is  necessary  to  install  proper 
metallic  filters  or  strainers  in  the  gasoline  feed  system,  in 
order  to  prevent  impurities  existing  in  the  gasoline,  from 
clogging  up  the  carburetor  jets. 

The  piping  systems  for  gasoline  and  oil  are  made  of 
copper.  The  joints  are  usually  of  rubber.  As  to  the  diam- 
eter of  the  piping  system,  it  must  be  comparatively  large 
for  the  oil,  in  order  to  avoid  obstruction  due  to  congealing. 
For  the  gasoline,  the  diameter  must  be  such  that  the  speed 
of  gasoline  flow  does  not  exceed  1  ft.  to  1.5  ft.  per  second; 
thus  for  instance,  supposing  an  engine  to  consume  24 
gallons  an   hour    (that   is,   0.00666   gallon  a   second)   the 


THE  ENGINE 


61 


inside  diameter  of  the  gasoline  pipe  must  be  from  ^{q  in. 
to  %  in. 

It  is  often  necessary  to  resort  to  special  radiators  to  cool 
the  oil.  On  the  contrary,  in  order  to  avoid  freezing,  in 
winter,  it  is  necessary  to  insulate  the  tank  with  felt. 

The  water  circulation  exists  only  in  water-cooled  engines. 
Fig.  57  shows  the  principle  of  the  water-cooling  system. 
The  engine  is  provided  with  a  water  pump  P,  which 
pumps  the  water  into  the  cylinder  jackets;  after  it  has  been 


^ 


!    Ill 


—Water-cooling  system. 

warmed  by  contact  with  the  cylinders,  it  flows  to  the  radi- 
ator R,  which  lowers  its  temperature.  Finally,  from  the 
radiator,  the  water  flows  back  to  the  pump,  and  the  circuit 
is  completed. 

The  gasoline  consumption  of  the  engines  varies  from  0.45 
to  0.55  lb.  per  H.P.  per  hour.  Assuming  an  average  of 
0.5  lb.  per  H.P.,  and  since  the  heat  of  the  combustion  of 
gasoline  is  about  18,600  B.t.u.  per  lb.,  then  for  1  H.P. 
per  hour,  9300  B.t.u.  are  necessary.  Now,  the  thermal 
equivalent  of  1  H.P.  per  hour  is  2550  B.t.u.,  therefore  only 

2550 

qoXTv  =  27.5  per  cent,  of  the  heat  of  combustion  of  the 


62  AIRPLANE  DESIGN  AND  CONSTRUCTION 

gasoline  is  utilized  in  useful  work;  the  rest,  72.5  per  cent,  or 
6550  B.t.u.  are  to  be  eliminated  through  exhaust  gases  or 
through  the  cooling  water.  The  B.t.u.  taken  up  by  the 
exhaust,  compared  with  those  taken  up  by  the  cooling  water, 
vary  not  only  for  each  engine,  but  even  for  each  type  of 
exhaust  system.  On  the  average,  we  can  assume  the  water 
to  absorb  about  30  per  cent,  of  the  B.t.u.,  or  about  2800 
B.t.u.  for  every  horsepower  per  hour;  the  quantity  of 
B.t.u.  to  be  absorbed  by  the  cooling  water  of  an  engine 
of  power  P,  is  consequently  equal  to  2800P   B.t.u. 

This  quantity  of  heat  must  naturally  be  given  up  to 
the  air,  and  the  radiator  is  used  for  that  purpose. 

From  the  standpoint  of  its  application  to  the  airplane,  the 
radiator  must  possess  tw^o  fundamental  qualities,  which  are : 

First,  it  must  be  as  light  as  possible,  and 

Second,  It  must  absorb  the  minimum  power  to  move  it 
through  the  air. 

Since  the  weight  also  involves  a  loss  of  power,  suppose 
that,  as  w^e  have  indicated,  the  flying  characteristics  depend 
on  the  weight  per  horsepower,  we  may  then  say  that  the 
lower  the  percentage  of  power  absorbed  the  more  efficient 
wdll  be  the  radiator.  It  is  possible  to  determine  experi- 
mentally the  coefficients  which  classify  a  given  type  of 
radiator  according  to  its  efficiency,  with  respect  to  its 
application  to  the  airplane. 

Before  all,  it  must  be  remembered  that  a  radiator  is 
nothing  more  than  a  reservoir  in  which  the  water  circulates 
in  such  a  way  as  to  expose  a  large  wall  surface  to  the  air 
which  passes  conveniently  through  it.  There  are  two  main 
types  of  radiators :  the  water  tube  type,  and  the  air  tube  or 
honeycomb  type.  In  the  first,  the  water  passes  through  a 
great  number  of  small  tubes,  disposed  parallel  to,  and  at 
some  distance  from  each  other;  the  air  passes  through  the 
gaps  between  the  tubes.  In  the  air  tube  radiators  (also 
called  honeycomb  radiators  because  of  their  resemblance 
to  the  cells  of  a  beehive),  the  water  circulates  through  the 
interstices  between  the  tubes,  while  the  air  flows  through 
the  tubes.     For  the  present  great  flying  speeds,  the  latter 


THE  ENGINE 


63 


type  of  radiator  has  proven  much  more  suitable,  and 
therefore  is  more  generally  used. 

To  compare  two  types  of  honeycomb  radiators,  we  will 
take  into  consideration  a  cubic  foot  of  radiator,  and  study 
its  weight,  water  capacity,  cooling  surface,  head  resistance, 
and  cooling  coefficient.  The  first  three  are  geometrical 
elements  which  can  be  defined  without  uncertainties. 

The  head  resistance  depends  not  only  on  the  speed  of 
the  airplane,  but  also  on  its  position  in  the  machine,  and 
frontal  area. 

Finally,  the  cooling  coefficient  beside  depending  on  the 
type  of  radiator,  depends  on  the  velocity  of  water  flow  and 
air  flow,  and  the  initial  temperatures  of  the  air  and  water. 
As  one  can  see,  there  are  many  factors  which  would  be 
difficult  to  condense  into  one  single  formula.  We  must 
therefore  content  ourselves  with  studying  separately,  the 
influence  of  each  of  the  above  factors. 

In  the  following  table  are  given  the  values  of  the  weight 
Wji,  water  capacity  W-^,  and  radiating  surface  S  per  cubic 
foot,  of  radiator  for  certain  types  of  radiators;  also  let  us 
call  a  the  ratio  between  the  weight  of  1  cu.  ft.  of  radiator 
including  the  water,  and  its  radiating  surface. 


Table  2 


Type  of  radiator 


Circular    tubes  with 

hexagonal  sides 
Square  tubes .... 

Square  tubes 

Hexagonal  tubes. 


Weight  Wr 
lb.  per  cu. 
ft. 


34.8 
38.9 
42.8 
29.7 


Water  capacity 

Ww  lb.  per  cu. 

ft. 


20.5 
9.3 

8.8 
12.9 


Total 

weight  W 

lb.  per   cu. 

ft. 


55.3 

48.2 
51.6 
42.6 


Radiating 

surface  2 

sq.  ft.  per 

cu.  ft. 


97.8 

188.5 
161.5 
132 


Total  weight 
of  radiating 
surface  lbs. 
per  sq.  ft. 


0.4660 
0.2653 
0.3095 
0.3227 


The  power  absorbed  by  the  head  resistance  of  1  cu.  ft. 
of  the  radiator,  may  assume  the  following  expression: 

where  S  is  the  frontal  area  of  the  radiator,  and  V  is  the 
speed  of  the  machine  in  feet  per  second. 


64  AIRPLANE  DESIGN  AND  CONSTRUCTION 


Let  us  call  d  the  de])th  of  the  radiator  core;  S  X  d  =  1 
1 
d' 


OT  S  =  J ;  thus  the  preceding  expression  becomes 


fixlxV  (1) 

a 

The  coefficient  /3  varies  not  only  with  the  different  types 
of  radiators,  but  with  the  same  radiator,  depending  on 
whether  it  is  placed  in  the  front  of  the  fuselage,  or  whether 
it  is  completely  surrounded  by  free  air. 

Equation  (1)  shows  that  to  decrease  the  head  resistance 
it  is  convenient  to  augment  the  depth  of  the  radiator  d. 
This  increase,  however,  is  Umited  by  the  fact  that  it  is 
advisable  to  keep  at  a  maximum  the  difference  in  the 
water  and  air  temperatures;  then  if  the  depth  of  the  radia- 
tor tubes  is  greatly  increased,  the  air  is  excessively 
heated,  thus  decreasing  the  difference  in  temperature 
between  it  and  the  water.  For  this  reason  the  depth  d 
may  become  greater  as  the  air  flow  v  through  the  tubes  is 
increased  in  velocity.  The  following  is  a  practical  formula 
that  may  be  used  in  determining  d : 

d  =  SXlXVv  (2) 

where  I  is  the  diameter  of  the  tubes  in  feet,  and  v  the  velocity 
of  the  air  flow^  through  the  tubes  in  feet  per  second. 

The  quantity  of  heat  radiated  by  1  cu.  ft.  of  radiator, 
not  only  depends  on  the  type,  but  on  the  difference  between 
the  temperature  t^  of  the  water,  and  t^  of  the  air,  on  the 
velocity  of  water  flow,  on  the  velocity  v  of  air  flow  through 
the  tubes,  and  on  the  radiating  surface  S  per  cubic  foot  of 
the  given  radiator. 

Assuming  the  velocity  of  water  flow  to  be  constant,  the 
quantity  of  B.t.u.  may  be  expressed  by 

yX  (L  -  L)  X  vi:  (3) 

where  y  is  the  cooling  coefficient,  varying  with  the  type  of 
radiator. 

Now,  if  the  engine  has  power  P,  the  radiator  must  take 


THE  ENGINE  65 

care  of  2800P  calories.     Therefore  the  volume  C   of  the 
radiator  must  be  such  that 

C  X  y  X  {ty,  -  ta)  X  V  X  ^  =  2800P 
or, 

^  2800P  ,4s 

yX{L-ta)XvX^ 

The   weight   of  the   radiator  will  be   C  X  W,   and   the 
power  absorbed  by  its  head  resistance  will  be 

CXBX\XV'     ^^^^  ^'' 


(5) 


d  SXlXVv 

If  we  call  ^  the  ratio  =^ »  the  power  required  to  carry 

D  Drag 

C  X  TFlb.  will  be  (in  ft.  lbs.), 

C  X  W  X  ^  X  7 

Therefore  the  total  power  absorbed  by  the  cooling  system 
will  be 

^  CX^XV       ^  ^  ^^r  x^XV 
SXlXVv  D 

and  by  equation  (4) 

P,  =  P  X  ,     ^^" X  \^+  W  X  |X  F 

yX{L-ta)XvX^      V^l\/v  D 

We  can  further  simphfy  the  preceding  expression.  First 
of  all  we  will  note  that  v  (the  velocity  of  air  flow  inside  of 
the  tubes),  is  proportional  to  the  speed  of  the  airplane;  we 
can  then  write 

V  =  8  X  V 

The  temperature  L  is  usually  taken  at  176°F.  (80°C.) ; 
it  is  not  convenient  to  increase  it,  as  the  airplane  must  be 
able  to  fly  at  considerable  altitude,  where  due  to  the  atmos- 
pheric depression,  the  boiling  point  of  water  is  lowered. 
For  the  air  temperature  ta,  we  must  take  the  maximum 
annual  value  of  the  region  in  which  the  machine  is  to  fly; 
in  cold  seasons,  the  cooling  capacity  of  the  radiator  becomes 


66  AIRPLANE  DESIGN  AND  CONSTRUCTION 

excessive,  and  therefore,  special  devices  are  resorted  to,  for 
cutting  off  part,  or  all  of  the  radiator. 

In  very  warm  climates,  we  may  take  for  example  <„  = 
104°,  then  the  result  is 

L  -  ta  =  176°  -  104°  =  72°F. 

As  to  the  dimension  I  (the  diameter  of  the  tube  through 
which  the  air  passes),  experiments  have  shown  that  to 
diminish  TF,  and  increase  2,  I  must  be  kept  around  0.396 

in.  =  0.033  ft.     Finally,  the  ratio  ^  for  a  good  wing,  varies 

p 
around  15.     Then   letting   p  =  ratio  ~^>   where  P/^  is  the 

power  absorbed  by  the  radiator,   and  P  the  total  power, 

W 
equation  (5),  remembering  that -;^  =  a,  by  the  proper  re- 
ductions, becomes 


"^        7  X  25'^  y  X  d 

where  the  coefficients  have  the  following  significance: 

Pr 
p  =  -p    =  percentage   of   power   absorbed   by  the 

radiator, 

W 
a  =  -:^  =  weight    of   radiator  per  square  foot   of 

radiating  surface, 
/3  =  coefficient  of  head  resistance, 

7  =  cooling  coefficient  of  the  radiator, 

8  =  y:  =  coefficient  of  velocity  reduction  inside  the 

tubes,  with  respect  to  the  speed  of  the  airplane, 
and 
2  =  radiating  surface  per  cubic  foot  of  radiator. 

C 
Similarly,  if  we  call  c  =  p  the  volume  of  radiator  re- 
quired per  horsepower,  and  simplifying  as  before,  equation 
(4)  gives 

'^■'        X 1  (7) 


7X2-5  V 


THE  ENGINE  67 

The  two  equations  (6)  and  (7),  allow  one  to  solve  the 
problem  of  determining  the  volume  of  the  radiator  and  the 
power  absorbed.  For  a  given  type  of  radiator,  a,  jS,  b, 
and  2  are  constants,  then  one  can  write 

149/3         _  ^.      583  X  a  _  ^.  38.9        ^    . 


TXSXa^^  '         7X5  '       y  X  8  X 

and  therefore  equations  (6)  and  (7)  become,  respectively, 

f  "^7  (8) 

I  p  =  5  X  7^^  +  C 

Naturally,  such  relations  can  be  used  within  the  present 
limits  of  airplane  speeds  (80  m.p.h.  to  160  m.p.h.).  They 
state  that  the  volume  of  the  radiator  is  inversely  propor- 
tional to  the  speed,  and  the  power  required  is  proportional 
to  the  M  power  of  the  speed. 

Before  leaving  the  discussion  on  radiators,  we  will  briefly 
discuss  the  systems  of  reducing  the  cooling  capacity.  There 
are  two  general  methods;  to  decrease  the  speed  of  water 
circulation,  or  to  decrease  the  speed  of  air  circulation. 
The  second  is  preferable,  and  is  today  more  generally 
adopted.  It  is  effected  by  providing  the  front  face  of  the 
radiator  with  shutters  which  can  be  more  or  less  closed 
until  the  air  passage  is  completely  obstructed. 

Mufflers  have  not  as  yet  been  extensively  adopted  for 
aviation  engines,  principally  because  they  entail  a  direct 
loss  of  power  amounting  to  from  6  per  cent,  to  10  per  cent.; 
and  because  of  their  bulk  and  weight.  Ordinary  exhaust 
tubes  are  used,  exhausting  singly  for  each  cylinder,  or 
joined  together,  the  point  being,  to  convey  the  gases  away 
from  those  parts  of  the  machine  that  might  be  damaged 
by  them. 

Before  concluding  this  chapter,  it  is  desirable  to  note  the 
functioning  of  the  engine  at  high  altitudes.  Modern  air- 
planes have  attained  heights  up  to  25,000  ft.;  battleplanes 
carry  out  their  mission  at  heights  varying  from  10,000  to 
20,000  ft.,  therefore  it  is  necessary  to  study  the  actions  of  the 
engine  at  such  altitudes. 


68 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Since  the  density  of  the  air  decreases  as  one  rises  above  the 
ground,  according  to  a  logarithmic  law,  let  H  be  the  height 
in  feet,  at  some  point  in  the  atmosphere  above  sea  level, 
and  fi  the  ratio  between  the  density  at  height  H,  and  that 
at  ground  level;  then 

H  =  60,720  log  ^ 

Fig.  58  shows  the  diagram  for  /i  as  a  function  of  H,  con- 
structed on  the  basis  of  the  preceding  formula. 


wouy 

~ 

~ 

~ 

~ 

~" 

■" 

~ 

~ 

— 

~ 

~ 

~ 

~ 

~ 

27000 

- 

- 

/ 

- 

> 

H- 60  720  loq-h 

- 

r 

?I000 

' 

/ 

^ 

.      13000 

/ 

" 

- 

/ 

/ 

^      15000 

/ 

/ 

c 

/ 

X.      12000 

/ 

^ 

' 

9000 

,/ 

/ 

/ 

6000 

/ 

/ 

3000 

/ 

/ 

y 

Ll 

0 

Iz 

L 

\_ 

L 

\_ 

L 

L 

_ 

L 

L 

_ 

_ 

_ 

_ 

P3 


Fig.  58. 


In  practice,  however,  it  happens  that  the  temperature  of 
the  air  also  decreases  as  one  rises  above  the  ground.  Then 
at  a  given  height  H,  the  density  /x  with  respect  to  the  ground 
level,  is  greater  than  the  value  given  by  the  above  formula. 
In  the  following  discussion,  which  is  primarily  qualitative  in 
nature,  we  will  not  take  into  account  this  decrease  in  tem- 
perature, in  order  not  to  complicate  the  treatment  of  the 
subject. 

With  this  foreword,  let  us  remember  that  the  moving 


THE  ENGINE 


69 


power  P,  is  equal  to  the  product  of  the  angular  velocity  co 
by  the  engine  torque  M. 

P  =  o^XM 

At  height  H,  the  engine  torque  M  is  proportional  to  the 


q.70o 


0.500 


0.100 


5000  lOOOO         15O0O  20000       25000 

H    .n   Feet 
FiG.  59. 


mass  of  oxygen  burned  in  one  unit  of  time,  or  to  the  density 
of  the  air.     Therefore 

P  =  ^ilf^eo  =  ^xFoX-  (1) 

Wo 

where 

Po  =  oioMo  =  power  at  sea  level. 

It  is  obvious  then,  that  as  the  machine  climbs,  the  power  of 
the  engine  decreases. 


70  AIRPLANE  DESIGN  AND  CONSTRUCTION 

In  Fig.  59,  a  diagram  is  given  for  the  reduction  in  per- 

P 

centage  ^  of  the  power,  corresjionding  to  the  increase  of  //. 

JL    o 

In  one  of  the  following  chapters  will  be  shown  the  in- 
fluence that  the  decrease  in  the  air  density  exerts  on  the 
power  required  for  the  sustentation  of  the  machine.  It 
will  be  readily  perceived,  that  if  a  machine  is  to  climb 
25,000  ft.,  it  must  be  able  to  maintain  itself  in  the  air  with 
0.251  of  the  power  of  the  engine;  in  other  words,  it  must 

carry  an  engine  which  will  develop  „  ^.^  =  =  4  times  the 

U.zol 

minimum   power   strictly   necessary  for  its   sustentation. 

In  practice,  these  are  the  actual  means  chosen  by  designers 

to   attain    high    altitudes.     That    is,    the    machines    are 

equipped  with   engines   of   such   excess   power,   as   to   be 

sufficient  to  maintain  flight  even  after  the  strong  reduction 

of  power  mentioned  above. 

Such  a  method  is  evidently  irrational,  since  at  ground 
level  the  airplane  employs  a  useless  excess  of  power,  while 
at  high  altitudes  it  is  overloaded  with  a  weight  of  engine 
entirely  out  of  proportion  to  the  power  actually  developed. 

To  eliminate  this  loss  of  efficiency,  tw^o  solutions  present 
themselves.  One  provisional  solution  (but  of  inestimable 
value  in  augmenting  the  efficiency  of  engines  as  they  are 
actually  conceived  and  constructed)  consists  of  providing 
the  engine  with  an  air  compressor  which  will  feed  the  car- 
buretor. In  this  way,  the  mass  of  gas  mixture  taken  in  by 
the  engine  at  each  admission  stroke,  is  greater  than  the 
amount  which  would  be  sucked  in  from  the  atmosphere 
directly,  and  as  a  result,  the  engine  torque  is  increased. 

Two  types  of  compressors  have  thus  far  been  experi- 
mented with;  the  turbo  compressor  designed  by  Rateau 
(France),  actioned  by  means  of  the  exhaust  gases,  and  the 
centrifugal  multiple  compressor  designed  by  Prof.  Anastasi 
(Italy),  actioned  by  the  engine  shaft. 

The  latter  type,  for  example,  with  an  increase  in  weight 
of  less  than  10  per  cent.,  allows  a  complete  recuperation  of 
the  power  at  13,000  ft.,  or  it  recuperates  50  per  cent,  of  the 


THE  ENGINE  71 

power.  Since  it  absorbs  10  per  cent,  of  the  power  in 
operation,  the  actual  power  recuperated  is  40  per  cent. 

These  compressors  have  not  yet  been  adopted  for  practi- 
cal use,  because  of  reasons  inherent  to  the  operation  of  the 
propeller,  which  will  be  seen  in  the  following  chapter. 

The  second  solution  (the  one  toward  which  engine 
technique  must  inevitably  direct  itself  in  order  to  open  a 
way  for  further  progress),  consists  in  predisposing  the 
engines  so  that  the  compression  of  air  at  high  altitudes 
may  be  effected  without  the  aid  of  external  compressors. 


CHAPTER  VI 
THE  PROPELLER 

The  propeller  is  the  aerial  propulsor  universally  adopted 
in  aviation. 

Its  scope  is  to  produce  and  maintain  a  force  of  traction 
capable  of  overcoming  the  various  head  resistances  of  the 
wings  and  other  parts  of  the  airplane. 

Calling  T  the  propeller  traction  in  pounds,  and  V  the 
velocity  of  the  airplane  in  feet  per  second,  the  product  T  X 
V  measures  the  useful  work  in  foot  pounds  per  second 
accomplished  by  the  propeller.  If  Po  is  the  power  of  the 
engine  in  horsepower,  the  propeller  efficiency  is  expressed 

by 

TV 

^  "  550  X  Po  ^^'' 

Every  effort  must  of  course  be  used  in  making  the  pro- 
peller efficiency  as  high  as  possible.  In  fact,  equation  (1) 
may  also  be  written  as 

P_     TV 
550  X  p 
which  means  that  having  assumed  a  given  speed  and  a  given 
head  resistance,  the  power  required  for  flight  will  be  so  much 
greater  as  the  value  of  p  is  smaller.     Suppose  for  example 
that  T  =  500  lb.  and  V  =  200  ft.  per  sec,  then 

for  PI  =  0.70  Pi  =  260  H.P. 

for  p2  =  0.80  P.  =  227  H.P. 

and  P2  is  13  per  cent,  less  than  Pi. 

A  propeller  is  defined  by  a  few  geometric  elements,  and 
by  its  operating  characteristics. 

The  geometric  elements  of  a  propeller  are  the  number  of 
blades,  the  diameter,  the  pitch,  the  maximum  width  of 
the  blades  and  their  profile. 

72 


THE  PROPELLER 


73 


Propellers  are  built  with  2,  3,  and  4  blades.  The  type 
most  commonly  used  is  the  2-blade  propeller,  especially 
when  quick-firing  guns  with  synchronized  devices  for  firing 
through  the  propeller,  are  mounted  on  the  airplane.  On 
machines  that  have  their  propellers  in  front,  the  problem 
of  firing  directly  forward  is  solved  by  equipping  the  machine 
guns  with  special  automatic  devices  operated  by  the  engine 


Fig.   60. 

(devices  called  synchronizers),  which  release  the  projectiles 
at  the  instant  the  propeller  blades  have  passed  in  front  of 
the  machine  gun  muzzle;  in  other  words,  the  projectile 
is  fired  through  the  plane  of  rotation  of  the  propeller  when 
the  blade  has  rotated  by  an  angle  a  (Fig.  60).  Angle  a 
is  not  fixed,  but  varies  with  the  number  of  revolutions  of  the 
propeller,  which  is  easily  understood  if  one  considers  that 


the  velocity  of  the  projectile  remains  constant,  while  the 
angular  velocity  of  the  propeller  varies.  Thus,  as  the 
number  of  revolutions  change,  there  is  a  dispersion  of  pro- 
jectiles; these  fall  in  a  sector  8,  which  is  called  the  angle  of 
dispersion  of  the  synchronizer  (Fig.  61).  Now,  if  this 
angle  is  greater  than  90°,  as  it  often  happens,  it  is  impossible 
to  use  4-bladed  propellers,  altho  in  certain  cases,  4-bladed 


74 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


propellers  may  be  convenient  for  reasons  of  efficiency,  as 
will   be   observed   further  on. 

The  diameter  of  the  propeller  depends  exclusively^  upon 
the  power  the  propeller  has  to  absorb,  and  upon  its 
number  of  revolutions. 

The  pitch  of  the  propeller,  from  an  aerodynamical  point 
of  view,  should  be  defined  as  "the  distance  by  which  the 
propeller  must  advance  for  every  revolution  in  order  that  the 
traction  be  zero.^^  In  practice,  however,  the  pitch  is  measured 
by  the  tangent  of  the  angle  of  inclination  of  the  propeller 
blade  with  respect  to  its  plane  of  rotation;  if  d  is  the  angle 
for  a  cross  section  AB  of  the  propeller,  at  a  distance  r  from 


Fig.  62. 

the  axis  XX  (Fig.  62),  the  pitch  of  the  propeller  at  that 
section  will  be 

p  =  2-Kr  tang  6 

Practically,  propellers  are  made  with  either  a  constant 
pitch  for  all  sections,  or  a  more  or  less  variable  one.  Figs. 
63  and  64  illustrate  respectively,  two  examples  of  propellers, 
one  with  constant  pitch,  the  other  with  variable  pitch. 

The  width  of  the  blade  is  not  important  as  to  its  absolute 
value,  but  is  important  with  respect  to  the  diameter. 
Since  the  propeller  blade  may  be  considered  as  a  small  wing 
moving  along  an  helicoidal  path,  it  is  evident  that  to 
increase  the  efficiency,  it  is  convenient  to  reduce  the  width 
of  the  blades  to  a  minimum  with  respect  to  the  diameter. 
However,  it  is  not  possible  to  reduce  the  blade  width  below 
a  certain  limit,  for  reasons  of  construction  and  resistance  of 


THE  PROPELLER 


75 


the  propeller.     Practically,  it  oscillates  from  8  to  10  per 
cent,  of  the  diameter. 

The  profile  of  a  propeller,  although  varying  from  section 
to  section,  characterizes  the  type  of  the  propeller.  It 
bears  a  great  influence  on  the  characteristics  of  a  propeller. 


Fig.   G3. 

All  propellers  having  the  same  type  of  profile,  are  said  to 
belong  to  the  same  family. 

Numerous  laboratory  experiments  on  propellers,  by 
Colonel  Dorand,  have  demonstrated  that  there  exist  cer- 
tain well-determined    relations    between  the  elements  of 


Fig.  64. 

propellers  that  are  of  the  same  family  and  geometrically 
similar,  so  that  once  the  coefficients  of  these  relations  are 
known,  it  is  easily  possible  to  obtain  all  the  data  for  the 
design  of  the  propeller.     Let 

D    =  the  diameter  of  the  propeller  in  feet, 

p    =  the  pitch  of  the  propeller  in  feet, 

Po  =  the  power  absorbed  by  the  propeller  on  the  ground, 


76 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


N   =  number  of  revolutions  per  second, 

V   =  the  speed  of  the  machine  in  feet  per  second,  and 

p    =  the  efficiency  of  the  propeller, 

than  the  relations  binding  the  preceding  parameters  are 


irnD 


(1) 

(2) 
(3) 


Equation  (2)  states  that  the  coefficient  a  of  equation  (T 

V 


IS  not  a  constant,  but   depends   on   the   ratio 


■nD 


Let 


us   examine   the    graphical    interpretation    of    this   ratio. 


V 

Since  -kiiD  is  the  peripheral  speed  of  the  blade  tip,  — ^ 

measures  the  angle  d  that  the  path  of  the  blade  tip  makes 

with  the  plane  of  rotation  of  the  propeller  (Fig.  65).     Now, 

the  angle  of  incidence  i  of  the  blade  with  respect  to  its  path, 

is  measured  exactly  by  the  difference  B  —  d';  as  6  is  fixed, 

i  varies  with  the  variation  of  6' ;  this  explains  why  as  tan- 

y 
gent  d'  =  — ^  varies,  the  power  absorbed  by  the  propeller 

varies,  and  consequently  coefficient  a  varies.     This  also 

explains   equation    (3),    which   shows   that   the   propeller 

V 
efficiency  is  dependent  upon  - — ^;  in  fact,  as  in  the  case  of 

a  wing,  the  efficiency  of  a  propeller  blade  varies  with  the 
variation  of  the  angle  of  incidence  i. 


THE  PROPELLER 


77 


Returning  to  equation  (1),  and  assuming  a  given  value 
for  a,  for  instance,  a  =  3  X  10"^  then  that  equation 
becomes 

P„  =  3  X  10-«  nW 
and  states 

1.  For  a  propeller  of  a  given  diameter,  the  power  required 
to  rotate  it,  increases  as  the  3d  power  of  n.  In  Fig.  66 
a  curve  is  drawn  illustrating  that  law,  assuming  D  =  10 
ft.;  the  curve  is  a  cubic  parabola. 


1000 
900 
&00 
TOO 
•  &00 
500 
400 
300 
200 


r 

1 

/ 

r 

y 

, 

' 

'   '    'o'   i^-a'  '   ' 

/ 

D=^  lOFt.. 

> 

/ 

> 

/ 

/ 

> 

/ 

J 

j^ 

'  1 

V 

' 

tf' 

?'^  -* 

/ 

/ 

X 

X 

^ 

^ 

^ 

Ml 

J 

" 

15  20  25 

n    in    R.p.s. 
Fig.  66. 


2.  For  a  given  number  of  revolutions,  the  power  required 
to  rotate  a  propeller,  increases  as  the  5th  power  of  the 
diameter. 

In  Fig.  67  the  curve  is  drawn  illustrating  that  law  for 
n  =  25  r.p.s.  =  1500  R.P.M.  It  is  a  parabola  of  the  5th 
degree. 

3.  Assuming  the  power,  the  diameter  to  be  given  to  the 
propeller  is  inversely  proportional  to  the  ^i  power  of  the 
number  of  revolutions.  The  curve  for  that  law  is  drawn  in 
Fig.  68.     It  is  an  hyperbola. 


78  AIRPLANE  DESIGN  AND  CONSTRUCTION 


400 --- 

HH 

P=  3x10  ^2SxD 

i  - 

300 :::::::::::: 

:::|::;  =  ::::::::::;^(::: 

200 --- 

lililB 

100 '    " 

:::::::::::-r:::::::::4 

:   ::::::;:i_;::::::::::::: 

< 

n 1:--  =  :^ : 

fflfflwiiiiiiiiiiiiiiiiy 

OI234567&9  10 

Diameter  ,Ft. 

Fig.  67. 


tu 

1 

1 

n 

1 

.-a 

\ 

P=  300  Up. 
300=3xlO'^An^^D^ 

\ 

\ 

1 

k 

20 

1 

" 

. 

N 

, 

«  , 

s 

_ 

_ 

_ 

__ 

._ 

__ 

_ 

_ 

_ 

_ 

__ 

_ 

_ 

!, 

^ 

_ 

__ 

- 

- 

- 

-- 

-- 

-^ 

- 

- 

- 

- 

-- 

- 

- 

- 

- 

^ 

- 

- 

- 

- 

10 

0  5  10  5  20  25 

n     R.p.s 

Fio.  68. 


THE  PROPELLER 


79 


Equation  (2),  which  gives  a  as  a  function  of  — ^'   is 

of  interest  only  inasmuch  as  it  is  necessary  to  know  the 
value  of  a  for  equation  (1).  Therefore,  we  shall  not  pause 
in  examination  of  it. 


riR                         P 

0.8                     -  p  = 

nT 

^ 

;^^1-s 

^^ 

^' 

' 

O  K 

^^ 

^^ 

ClA. 

^'^ 

"^^ 

0.3                        . 

/ 

0?                 ^         - 

0.2            ^y 

0!       ^<                - 

n  ^ 

0.05 


0.10 


015 


020    0.227025 


O30 


0.35 


V 
Fig.  69. 


l.V 

~ 

~ 

"■ 

~ 

~ 

~^ 

~ 

~ 

" 

~ 

' 

p 

J 

_, 

_ 

^ 

■^ 

N 

-\ 

^  ^ 

1 

if* 

1 

^ 

1 

' 

^ 

•■ 

0/ 

^ 

/* 

^  "^ 

, 

7 

' 

/' 

-     ^^ 

j 

,,^ 

*\ 

n2' 

J 

.. 

_J 

_ 

U 

-J 

_]_ 

.. 

.. 

0.05 


0.15  020 

V 
TtnO 

Fig.  70. 


0.25 


0.30 


035 


On  the  contrary,  it  is  of  maximum  interest  to  examine 

equation  (3),  which  gives  the  efficiency  of  the  propeller. 

Let  us  consider  all  geometrically  similar  propellers  of 

the  same  family,  having  diameter  D  and  pitch  p,  so  that  ^ 


80  AIRPLANE  DESIGN  AND  CONSTRUCTION 

=  0.8;  Fig.  69  gives  the  diagram  p  = /of — v^)   for  such 

propellers.     The    diagram    shows    that    p    increases    and 
reaches  a  maximum  value  pmax  =  0.71   corresponding  to 

V 
the  value  — ^  =  0.227. 

Let  us  now  consider  a  group  of  propellers  also  of  similar 

P 
profile,  but  having  j^  =  1.0,  and  let  us  draw  the  efficiency 

diagram  (Fig.  70).     This  will  be  similar  to  the  preceding 
one  in  shape,  but  will  reach  a  value  p„,ax  =  0.77  corre- 

V 
spending  to  a  value  of  - — ^  =  0.275. 

P 
If  this  experiment  is  repeated  for  various  values  of  ^s' 

it  will  be  observed  that  the  maximum  efficiency  obtainable 

from  a  propeller  of  certain  profile,  varies  with  the  variation 

of  that  ratio;  it  is  easy  to  construct  a  diagram  giving  all  the 

P 
values  of  pmax  as  functions  of  j^-     Such   a   diagram  shows 

that  a  propeller  of  a  certain  type,  gives  its  maximum  effi- 

P 
ciency  when  yc  =  1.20.     Naturally  this  condition  does  not 

suffice,  as  the  propeller  must  rotate  at  a  number  of  revolu- 

V 
tions  n,  such  that  the  ratio  — f^  will  be  the  one  at  which 

the  propeller  actually  attains  the  maximum  efficiency. 

p 
Fig.  71  gives  the  values  of  ^>  a,  and  p,  as  functions  of 

V 
— j::,  for  the  best  propellers  actually  existing. 

The  use  of  these  diagrams  requires  a  knowledge  of  all  the 

aerodynamical  characteristics  of  the  machine  for  which  the 

propeller  is  intended.     However,  even  a  partial  study  of 

them  is  very  interesting  for  the  results  that  can  be  attained. 

p  V 

First,  we  see  that    for  ^  =  1.18  and  — ^  =  0.32,  the 

maximum   efficiency  p  reaches  a  value  of   82   per  cent. 
Obviously  that  is  very  high,   especially  when  the  great 


THE  PROPELLER 


81 


simplicity  of  the  aerial  propeller  is  considered.  But  un- 
fortunately, it  often  occurs  in  practice,  that  this  value  of 
efficiency  cannot  be  attained  because  there  are   certain 


7x10-^ 


6x10 


5x10' 


3x10 


J 
'   S 


Oaaaatmillllllll Il IIIIMIIIIIIIimimnmTTTTTTTTTTmiMM 0 

014       0.16       0.18        0.20       0.22       0.24       0.26       0.2&       Q30      032 

V 

TtnD 

Fig.   71. 

parameters  which  it  is  impossible   to  vary.     An  example 
will  illustrate  this  point. 

Let  us  assume  that  we  have  at  our  disposition  an  engine 


82  AIRPLANE  DESIGN  AND  CONSTRUCTION 

developing  300  H.P.,  while  its  shaft  makes  25  r.p.s.,  and  let 
us  assume  that  we  wish  to  adopt  such  an  engine  on  two 
different  machines,  one  to  carry  heavy  loads  and  conse- 
quently slow,  the  other  intended  for  high  speeds.  Let  the 
speed  of  the  first  machine  be  125  ft.  per  sec,  and  that  of 
the  second  200  ft.  per  sec.  We  shall  then  determine  the 
most  suitable  propeller  for  each  machine. 

For  the  first  machine,  as  n  =  25,  and  V  =  125,  the  ex- 
pression —^  becomes  equal  to  k  •  We  must  choose  a 
value  of  D,  such  that  together  with  the  value  of  a  corre- 
sponding to-^-,  (Fig.  71),  it  will  satisfy  the  equation 

300  =  anW" 
or,  for  n  =  25 

a  X  D'  ^  0.0192 

Now  the  corresponding  values  of  a  and  D  satisfying  those 
equations  are 

a  =  ^^1.4  X  10-"  and  D  =  10.7;  in  fact,  for  this  value  of  D, 

^  =  3.14X25^X107  =  '^^•^^^'  *^  '''^''^  corresponds 
a  =  1.4  X  10"^;  the  corresponding  value  of  p  is  ~0.62, 

that  is,  our  propeller  will  have  an  efficiency  of  62  per  cent. ; 

its  pitch  will  be  0.46  X  10.7  =5.0  ft. 

For   the    second    machine   instead — n  =  25,   and    V  = 

«^^     .t.  .  ^    !_  200  2.55 

200-the  expression  ,;^  becomes  3-^^^25^^^  =  -^ 

and  a  X  D^  =  0.0192;  the  two  values  satisfying  the  desired 
conditions  are 

V  200 

^  =  •UOr25-X8r6  =  0-296;  «  =  4.1  X  10-, 

and  corresponding  to  these  values  p  =  0.79.     The   pitch 

results  equal  to  9.3  ft. 

We   can  see  then,   that   the   propeller  for  the   second 

79 
machine,  has  an  efficiency  of  79  per  cent. ;  that  is  ..^  = 

'^1.27  more  than  that  of  the  first  machine.     It  would  be 


THE  PROPELLER  83 

possible  to  improve  the  propeller  efficiency  of  the  first 
machine  by  using  a  reduction  gear  to  decrease  the  number 
of  revolutions  of  the  propeller.  In  this  case,  it  would  even 
be  possible  by  properly  selecting  a  reduction  gear,  to  attain 
the  maximum  efficiency  of  82  per  cent. 

But  this  would  require  the  construction  of  a  propeller 
of  such  diameter,  that  it  could  not  be  installed  on  the 
machine.  Consequently  we  shall  suppose  a  fixed  maximum 
diameter  of  14  ft.     Then  it  is  necessary  to  find  a  value  of 

V 

n,  such  that  value  a  corresponding  to      ^  gives 

a  X  n^  X  D"  =  300.     That  value  is  n  =  12.4  r.p.s., 
Y 
for  which  — ^  =  0.23  and  p  =  0.72.     We  see  then  that  m 

0.72 
this  case,  the  reduction  gear  has  gained  p.  ^o  ^  ^-^^  °^    ^^ 

per  cent,  of  the  power,  which  may  mean  16  per  cent,  of 
the  total  load;  and  if  w^e  bear  in  mind  that  the  useful  load 
is  generally  about  H  of  the  total  weight,  we  see  that  a 
gain  of  16  per  cent,  on  the  total  load,  represents  a  gain  of 
about  50  per  cent,  on  the  useful  load;  this  abundantly 
covers  the  additional  load  due  to  the  reduction  gear. 

From  the  preceding,  we  see  that  in  order  to  obtain  good 
efficiency,  modern  engines  whose  number  of  revolutions 
are  very  high,  must  be  provided  with  a  reduction  gear 
when  they  are  to  be  applied  to  slow  machines.  On  the 
contrary,  for  very  fast  machines,  the  propeller  may  be 
directly  connected,  even  if  the  number  of  revolutions  of  the 
shaft  is  very  high. 

Concluding  we  can  say,  that  it  is  not  sufficient  for  a 
propeller  to  be  well  designed  in  order  to  give  good  efficiency, 
but  it  is  necessary  that  it  be  used  under  those  conditions  of 
speed  V  and  number  of  revolutions  n,  for  which  it  will 
give  good  efficiency. 

Until  now  we  have  studied  the  functioning  of  the  propel- 
ler in  the  atmospheric  conditions  at  sea  level.  Let  us  see 
what  happens  when  it  operates  at  high  altitudes.  The 
equation  of  the  power  then  becomes 

'P  =  aXaXn'XD' 


84  AIRPLANE  DESIGN  AND  CONSTRUCTION 

where  /x  is  the  ratio  between  the  density  at  the  height  under 
consideration  and  that  on  the  ground  (see  Chapter  5). 
This  means  that  the  power  required  to  rotate  the  propeller 
decreases  as  the  propeller  rises  through  the  air,  in  direct 
proportion  to  the  ratio  of  the  densities. 

As  to  the  number  of  revolutions,  the  preceding  equation 
gives 

P 

Theoretically,  the  power  of  the  engine  varies  proportion- 
ally to  yu,  that  is 

so  that  theoretically  we  should  have 

3    ^    JJ^Po      ^  Po 

and  this  would  mean  that  the  number  of  revolutions  of  the 
propeller  would  be  the  same  at  any  height  as  on  the  ground. 
Practically,  however,  the  motive  power  decreases  a  Uttle 
more  rapidly  than  proportionally  to  m  (see  Chapter  5) ,  and 
consequently  the  number  of  revolutions  slowly  decreases  as 
the  propeller  rises  in  the  air. 

If  instead,  by  using  a  compressor  or  other  device,  the 
power  of  the  engine  were  kept  constant  and  equal  to  Po, 
then  the  number  of  revolutions  would  increase  inversely 
as  \/;u.     So  for  instance,  at  14,500  ft.,  where  m  =  0.5  the 

n  n 

revolutions  would  be    y^_  =  tt^^  =  1.26  n.     A  propeller 

making  1500  revolutions  on  the  ground,  would  make  1900 
revolutions  at  a  height.  This,  then,  is  one  of  the  principal 
difficulties  that  have  until  now  opposed  the  introduction  of 
compressors  for  practical  use.  In  fact,  as  it  is  unsafe  that 
an  engine  designed  for  1500  revolutions  make  1900,  it 
would  practically  be  necessary  for  the  propeller  to  brake 
the  engine  on  the  ground,  so  as  not  to  allow  a  number  of 
revolutions  greater  than  1500  X  0.79  =  1180.  In  this 
way,  however,  the  engine  on  the  ground  could  not  develop 


THE  PROPELLER  85 

all  its  power,  and  therefore  the  characteristics  of  the 
machine  would  be  considerably  decreased. 

To  eliminate  such  an  inconvenience,  there  should  be  the 
solution  of  adopting  propellers  whose  pitch  could  be  vari- 
able in  flight,  at  the  will  of  the  pilot;  thus  the  pilot  would 
be  enabled  to  vary  the  coefficient  of  the  formula 

P  =  aXn^  X  D^ 

and  consequently  could  contain  the  value  of  n  within 
proper  limits.  Today,  the  problem  of  the  variable  pro- 
peller has  not  yet  been  satisfactorily  solved;  but  tentatives 
are  being  made  which  point  to  positive  results. 

The  materials  used  in  the  construction  of  propellers,  the 
stresses  to  which  they  are  subjected,  and  the  mode  of 
designing  them,  will  be  dealt  with  in  Part  IV  of  this  book. 


PART  II 
THE  AEROPLANE  IN  FLIGHT 


CHAPTER  VII 
ELEMENTS  OF  AERODYNAMICS 

Aerodynamics  studies  the  laws  governing  the  reactions 
of  the  air  on  bodies  moving  through  it. 

Very  few  of  these  laws  can  be  established  on  a  basis  of 
theoretical  considerations.  These  can  only  give  indications 
in  general;  the  research  for  coefficients,  which  are  definitely 
those  of  interest  in  the  study  of  the  airplane,  cannot  be 
completed  except  in  the  experimental  field. 


Direction  Perpendicular' 
to  Line  ofFligh-f-and 
Coniafned  in  ihe  Yerhical 
Plane. 


Direci-ion  Perpend icularfo  the 
VerHcal  Plane  Containing  the 
f^^.^    LineofFnghh 


For  these  reasons,  we  shall  consider  aerodynamics  as  an 
"Applied  Mechanics"  and  we  shall  rapidly  study  the 
experimental  elements  in  so  far  as  they  have  a  direct 
application  to  the  airplane. 

Let  us  consider  any  body  moving  through  the  air  at  a 
speed  V,  and  let  us  represent  the  body  by  its  center  of 
gravity  G  (Fig.  72).  Due  to  the  disturbance  in  the  air, 
positive  and  negative  pressure  zones  will  be  produced  on  the 
various  surfaces  of  the  body,  and  in  general,  the  resultant 

87 


88 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


R  of  these  pressures,  may  have  any  direction  whatever. 
Let  us  resolve  that  resultant  into  three  directions  perpen- 
dicular to  one  another,  the  first  in  the  sense  of  the  Hne  of 
flight,  the  second  perpendicular  to  the  line  of  flight  and 
lying  in  the  vertical  plane  passing  through  the  center  of 
gravity,  and  the  third  perpendicular  to  that  plane. 

These  components  R^,  R^,  and  R's,  shall  be  called 
respectively : 

R^,  the  Lift  component, 

Rg,  the  Drag  component, 

R\,  the  Drift  component, 


RaR 


Fig.  73. 


If  we  wished  to  make  a  complete  study  of  the  motion  of  the 
body  in  the  air  it  would  be  necessary  to  know  the  values,  of 
7?x,  R5,  and  R\,  for  all  the  infinite  number  of  orientations 
that  the  body  could  assume  with  respect  to  its  line  of  path; 
practically,  the  most  laborious  research  work  of  this  kind 
would  be  of  scant  interest  in  the  study  of  the  motion  of  the 
airplane. 

Let  us  first  note  that  the  airplane  admits  a  plane  of  sym- 
metry, and  that  its  line  of  path  is,  in  general,  contained  in 
that  plane  of  symmetry;  in  such  a  case,  the  component  R\ 
=  0.  This  is  why  the  study  of  components  R^  and  Rs  is 
made  by  assuming  the  line  of  path  contained  in  the  plane 
of  symmetry,  and  referring  the  values  to  the  angle  i  that 
the  line  of  path  makes  with  any  straight  line  contained  in 
the  plane  of  symmetry  and  fixed  with  the  machine. 

In  general,  this  reference  is  made  to  the  wing  chord  (Fig. 


ELEMENTS  OF  AERODYNAMICS 


89 


73),  and  i  is  called  the  angle  of  incidence;  as  to  the  force  of 
drift,  usually  the  study  of  its  law  of  variation  is  made  by 
keeping  constant  the  angle  i  between  the  chord  and  the 
projection  of  the  line  of  path  on  the  plane  of  symmetry, 
and  varying  only  the  angle  5  between  the  line  of  path  and 
the  plane  of  symmetry  (Fig.  74) ;  the  angle  8  is  called  the 
angle  of  drift. 


Summarizing,  the  study  of  components  R^,  R^,  and  R's, 
is  usually  made  in  the  following  manner: 

1.  To  study  i?x  and  Rs,  considering  them  as  functions 
of  the  angle  of  incidence  i. 

2.  To  study  R's  by  considering  it  as  a  function  of  the 
angle  of  drift  5. 

For  the  study  of  the  air  reactions  on  a  body  moving 
through  the  air,  the  aerodynamical  laboratory  is  the  most 
important  means  at  the  disposal  of  the  aeronautical 
engineer. 

The  equipment  of  an  aerodynamical  laboratory  consists 
of  a  special  tube  system  of  more  or  less  vast  proportions, 


90 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


inside  of  which  the  air  is  made  to  circulate  by  means  of 
special  fans  (Fig.  75).     The  small  models  to  be  tested  are 


Fig.  75. 

suspended  in  the  air  current,  and  are  connected  to  instru- 
ments which  permit  the  determination  of    the  reactions 


OD 


.Z^ 


Fig.  76. 


provoked  upon  them  by  the  air.     The  section  in  which  the 
models  are  tested  is  generally  the  smallest  of  the  tube  sys- 


ELEMENTS  OF  AERODYNAMICS  91 

tern,  and  a  room  is  constructed  corresponding  to  it,  from 
which  the  tests  may  be  observed.  The  speed  of  the  air 
current  may  easily  be  varied  by  varying  the  number  of 
revolutions  of  the  fan. 

The  velocity  of  the  current  may  be  measured  by  various 
systems,  more  or  less  analogous.  We  shall  describe  the 
Pitot  tube,  which  is  also  used  on  airplanes  as  a  speed  indi- 
cator. The  Pitot  tube  (Fig.  76),  consists  of  two  concentric 
tubes,  the  one,  internal  tube  a  opening  forward  against 
the  wind,  the  other  external  tube  h,  closed  on  the  forward 
end  but  having  small  circular  holes.  These  tubes  are  con- 
nected to  a  differential  manometer.     The  pressure  trans- 

dV- 
mitted  by  tube  a  is  equal  to  P  +  ~2~'^  ^^^  pressure  trans- 
mitted by  tube  b  is  equal  to  P;  thus,  the  differential  man- 


ometer  will  indicate 

a  pressure  h  in  feet  of  air,  equal  to 

that  is 

^  2g        ^ 

consequently 

-f 

y__^M 

as  ^  =  32.2,  the  result  will  be 

^-^-ll 

d  represents  the  specific  weight  of  the  air.  The  preceding 
formula  consequently  gives  us  the  means  of  graduating  the 
manometer  so  that  by  using  the  Pitot  tube  it  will  read  air 
speed  directly. 

With  this  foreword,  let  us  note  that  experiments  have 
demonstrated  that  the  reaction  of  the  air  R,  on  a  body 
moving  through  the  air,  and  therefore  also  its  components 
Rx,  Rs  and  R's,  may  be  expressed  by  means  of  the  formula 

R  =  a  "^  X  A  X  V- 
U 


92  AIRPLANE  DESIGN  AND  CONSTRUCTION 

where 

a  =  coefficient  depending  on  the  angle  of  incidence 

or  the  angle  of  drift, 
d  =  the  specific  weight  of  the  air, 
g  =  is  the  acceleration  due  to  gravity  (which  at 

the  latitude  of  45°  =  32.2), 
A  =  the  major  section  of  model  tested  (and  defined 

as  will  be  seen  presently),  and 
V  =  the  speed. 
As  a  matter  of  convenience  we  shall  give  the  coefficients 
assuming  that  the  specific  weight  of  the  air  is  the  one  cor- 
responding to  the  pressure  of  one  atmosphere  (33.9  ft.  of 
water),  and  to  the  temperature  of  59°F.     Furthermore  the 
coefficients  will  be  referred  to  the  speed  of  100  m.p.h. 
Then  the  preceding  formula  can  be  written 


R  =  K  X  A  X 


im)''  (^^ 


and  knowing  K,  it  gives  the  reaction  of  the  air  on  a  body 
similar  to  the  model  to  which  K  refers,  but  whose  section 
is  equal  to  A  sq.  ft.,  and  the  speed  to  V  m.p.h. 

It  is  of  interest  to  know  the  value  of  coefficient  K, 
when  the  pressure  and  the  temperature  of  the  air  are  no 
more  1  atmosphere  and  59°  F.,  but  have  respectively  any 
value  h  whatsoever  (in  feet  of  water),  and  t°  (degrees  F.). 
The  value  of  the  new  coefficient  Kht  is  then  evidently  given 
by 

^''  ~  ^  ^  33:9  ^  TeoM^l^ 

This  equation  will  be  of  interest  in  the  study  of  flight 
at  high  altitudes. 

Interpreted  with  respect  to  the  speed,  formula  (1) 
states  that  the  reaction  of  the  air  on  a  body  moving  through 
it,  is  proportional  to  the  square  of  the  speed  of  translation. 
This  is  true  only  within  certain  limits.  In  fact,  we  shall 
soon  see  that  in  some  cases  coefficient  K,  determined  by 
equation  (1),  changes  with  the  variation  of  the  speed, 
although  the  angle  of  incidence  remains  constant. 


ELEMENTS  OF  AERODYNAMICS  93 

From  the  aerodynamical  point  of  view,  the  section  of 
the  parts  which  compose  an  airplane  may  be  grouped  in 
three  main  classes  which  are: 

1.  Surfaces  in  which  the  Lift  component  predominates, 

2.  Surfaces  in  which  the  Drag  component  predominates, 
and 

3.  Surfaces  in  which  the  Drift  component  predominates. 
The    first    are    essentially    intended    for   sustentation. 

Among  them,  the  elevator  is  also  to  be  considered,  of  which 
the  aerodynamical  study  is  analogous  to  that  of  the  wings. 

The  second,  surfaces  in  which  the  component  of  head 
resistance  exists  almost  solely,  are  the  major  sections  of 
all  those  parts,  as  the  fuselage,  landing  gear,  rigging,  etc., 
which  although  not  being  intended  for  sustentation,  form 
essential  parts  of  the  airplane. 

Finally,  the  last  surfaces  are  those  in  which  the  air 
reaction  equals  zero  until  the  line  of  path  is  contained  in 
the  plane  of  symmetry  of  the  airplane,  but  manifests  itself 
as  soon  as  the  airplane  drifts. 

In  Chapter  I,  we  have  spoken  diffusely  enough  of  the 
criterions  followed  for  the  aerodynamic  study  of  a  wing. 
Consequently,  we  shall  repeat  briefly  what  has  already 
been  said. 

Let  us  consider  a  wing  which  displaces  itself  along  a 
line  of  path  which  makes  an  angle  ^  with  its  chord ;  a  certain 
reaction  will  be  borne  upon  it  which  may  be  examined  in 
its  two  components  R^^  and  R^  respectively  perpendicular 
and  opposite  to  the  line  of  path,  and  which  shall  be  called 
Lift  and  Drag,  indicating  them  respectively  by  the  symbols 
L  and  D. 

We  may  then  write. 


^  =  ^  ^  ^  ^  {mj 


Vioo 

Where  the  coefficients  X  and  8  are  functions  of  the  angle 


94  AIRPLANE  DESIGN  AND  CONSTRUCTION 

of  incidence,  and  define  a  type  of  wing,  and  .1  is  the  total 
surface  of  wing.     The  wing  efficiency  is  given  by 

L  _  X 

D       5 

and  measures  the  number  of  pounds  the  wing  can  sustain 
for  each  pound  of  head  resistance. 

In  Chapter  I,  we  have  given  the  diagrams  for  X,  8  and 

->  as  functions  of  i  for  two  types  of  wings;  consequently, 

0 

it  is  unnecessary  to  record  further  examples. 

For  a  complete  aerodynamical  study  of  a  wing,  it  is 
necessary  to  determine  in    addition  to  the  diagrams  of 

X,  5  and  -'  as  functions  of  i,  also  the  diagram  of  the  ratio 

0 

X 

^  as  a  function  of  i,  which  defines  the  position  at  the  center 
of  pressure  (see  Chapter  II).     Knowledge  of  the  law  of 

X 

variation  of  ^  as  a  function  of  i,  is  necessary  to  enable  the 

study  of  the  balance  of  the  airplane. 

In  the  reports  on  aerodynamical  experiments  conducted 

in  various  laboratories,  American,  English,  Italian,  etc.,  the 

reader  will  find  a  vast  amount  of  experimental  material 

which  will  assist  him  in  forming  an  idea  of  the  influence 

borne  on  the  coefficients  X  and  5,  not  only  by  the  shape 

and  relative  dimensions  of  the  wings,  as   for  instance  the 

,.  span  ,  thickness  of  the  wing   ,    ^     , 

ratios  -T- — J — TTv -' —  and  — i       i    Frr • '  but  also 

chord  of  the  wmg  chord  of  the  wmg 

by  the  relative  positions  of  the  wings  with  respect  to  each 
other;  such  as  multiplane  machines  with  superimposed 
wings,  with  wings  in  tandem,  etc. 

In  the  study  of  coefficients  of  resisting  surfaces,  in  gen- 
eral, solely  the  knowledge  of  the  component  Rs  is  of  interest; 
the  sustaining  component  R^  is  equal  to  zero,  or  is  of  a 
negligible  value  as  compared  with  that  of  R^.  We  then 
have 


Rs  =  K  X  A  X 


Vioo/ 


ELEMENTS  OF  AERODYNAMICS 


95 


where  i^  is  a  function  of  i,  and  A  measures  the  surface  of 
the  major  section  of  the  form  under  observation,  taken 


K\V\\\\VVVV\\^V^        CD 


L^!Z3 


perpendicular  to  the  axis  of  symmetry  of  the  body,  or  to 
the  axis  parallel  to  the  normal  line  of  path. 


96 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


In  general,  the  head  resistance  is  usually  determined  for 
only  one  value  of  i,  that  is,  for  the  value  corresponding  to 
normal  flight.  In  fact,  it  should  be  noted  that  an  airplane 
normally  varies  its  angle  of  incidence  within  very  narrow 
hmits,  from  0°  to  10°;  now,  while  for  wings  such  variations 
of  incidence  bring  variations  of  enormous  importance  in 
the  values  of  L  as  well  as  in  those  of  D,  the  variation  of 
coefficient  K  for  the  resistance  surfaces  is  relatively  small. 
Consequently,  in  laboratories,  only  one  value  is  found. 
Nevertheless,  exception  is  made  for  the  wires  and  cables, 
which  are  set  on  the  airplanes  at  a  most  variable  inclina- 
tion, and  therefore  it  is  interesting  to  know  coefficient  K 
for  all  the  angles  of  incidence. 

A  table  is  given  below  compiled  on  the  basis  of  Eiffel's 
experiments,  which  gives  the  value  of  K  for  the  following 
forms  (Fig.  77),  and  for  a  speed  of  90  feet  per  second: 

A  =  Half  sphere  with  concavity  facing  the  wind, 

B  =  Plain  disc  perpendicular  to  the  wind, 

C  =  Half  sphere  with  convexity  facing  the  wind, 

D  =  Sphere, 

H  =  Cylinder  with  ends  having  plain  faces,  with  axis 
parallel  to  the  wind, 

/  =  Cyhnder  with  spherical  ends,  with  axis  parallel  to 
the  wind, 

E  =  Cylinder  with  axis  perpendicular  to  the  wind, 

F  =  Airplane  strut — fineness  ratio  }4, 

G  =  Airplane  strut — fineness  ratio  }i, 

L  =  Airplane  fuselage  with  radiator  in  front, 

M  =  Dirigible  shape, 

N  =  Airplane  wheel  without  fabric,  and 

0   =  Wheel  covered  with  fabric. 


Iable 

3 

A 

B 

C 

D 

E 

F 

G           H 

I 

L 

" 

JV 

0 

43.5 

28.6 

7.8^4.1 

8.7 

15.6 

3.5 

22.6 

6.1 

8 

8 

28 

14 

ELEMENTS  OF  AERODYNAMICS 


97 


In  the  above  table,  one  is  immediately  impressed  by 
the  very  low  value  for  the  dirigible  form.  Its  resistance 
is  about  10  times  less  than  that  of  the  plain  disc. 

The  preceding  table  contains  values  corresponding  to  a 
speed  of  90  ft.  per  sec.  If  the  law  of  proportion  to  the  square 
of  the  speed  were  exact,  these  values  would  also  be  available 
for  other  speeds.     On  the  contrary,  at  different  speeds  these 


wu 

■ 

50 

- 

^ 

40 

i^^SO 

20 

10 

■^ 

^v.. 

0 

0      10     20     30     40      50     60     70     &0     90     100     110  Speec^ 
Ft.  per  Sec. 
Fig.  78. 


values  vary.  An  example  will  better  illustrate  this  point. 
In  Fig.  78  diagrams  are  given  of  the  variation  of  K 
for  the  forms  A  and  D,  and  for  the  speed  of  from  13  to 
100  ft.  per  sec.  (Eiffel's  experiments).  We  see  that  coef- 
ficient K  of  form  A,  increases  with  the  speed,  while  that  of 
D  decreases.  These  anomalies  can  be  explained  by  admit- 
ting that  the  various  speeds  vary  the  vortexes  which  are 
formed  behind  the  bodies  in  question,  therefore  varying 
the  distribution  of  the  positive  and  negative  pressure 
zones,  and  consequently  the  coefficients  of  head  resistance. 


98 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Figs.  79  and  80  give  the  diagrams  of  the  coefficient  K,  for 
the  wires  and  cables  (Eiffel);  for  the  wires,  coefficient  K 
first  decreases,  then  increases;  for  the  cables  instead, 
the  value   of    K   shows    an    opposite    tendency.     Finally, 


30 

-^ 

___ 

- 

^^ZO 

10 

n 

0       10      20      30     40      50     60     70      30     90      100     110  Speed 
Ft.  per  Sec. 

Fig.  79. 


40 


30 


0      10     20      30    40      50     60    70     30     20     100     110  Speed 
Ft.  per  Sec. 

Fig.  80. 


Fig.  81  gives  the  diagram  showing  how  coefficient  K 
varies  for  the  wires  and  cables  when  their  angle  of  incidence 
varies  from  0°  to  90°. 

In  studying  the  airplane,  it  is  more  interesting  to  know 
the  total  head  resistance  than  that  of  the  various  parts; 


ELEMENTS  OF  AERODYNAMICS 


99 


if  we  call  Ai,  Ai,  .  .  .  and  A^  the  major  sections  of  the 
various  parts  constituting  the  airplane  and  which  produce 
a  head  resistance,  (fuselage,  landing  gear,  wheels,  struts, 
wires,  radiators,  bombs,  etc.),  and  Ki,  K^,   .    .    .   and  X„, 


1.0 


0.& 


,0.6 


0.4 


02 


00 


.^ 

J 

_/ 

y 

7 

t 

7 

r 

1 

t 

t 

J 

t 

7 

7 

15  30  45  eO  75  90 

Angle  of  Incidence  in  Degrees 
Fig.  81. 

the  respective  coefficients  of  head  resistance,  the  total  head 
resistance  R^  of  the  airplane  will  be 

fi.  =  if.A.Q^  +  AV4.  (4)>  .  .  .  X»A„Q' 

=  (ifiAi  +  KiA2  +  .  .  .  A'^„)(jQjjj    =  „  (jqqJ 


100  AIRPLANE  DESIGN  AND  CONSTRUCTION 

where  a  =  KiAi  +  K2A2  +  .  .  .  A'„.4„  and  is  called  the 
total  coefficient  of  head  resistance  of  the  airplane. 

As  to  the  study  of  the  drift  surfaces,  it  is  accomplished 
by  taking  into  consideration  only  the  drift  component,  and 
not  the  component  of  head  resistance,  as  the  latter  is 
negligible  with  respect  to  the  former.  Furthermore,  in 
this  study  it  is  interesting  to  know  the  center  of  drift  at 
various  angles  of  drift,  in  order  to  determine  the  moments 
of  drift  and  their  efficaciousness  for  directional  stability. 
When  the  line  of  path  lies  out  of  the  plane  of  symmetry, 
all  the  parts  of  the  airplane  can  be  considered  as  drift 
surfaces.  Nevertheless,  the  most  important  are  the  fusel- 
age, the  fin,  and  the  rudder.  From  the  point  of  view  of 
drift  forces,  the  fuselages  without  fins  and  without  rudders, 
may  be  unstable;  that  is,  the  center  of  drift  may  be  situated 
before  the  center  of  gravity  in  such  a  way  as  to  accentuate 
the  path  in  drift  when  this  has  been  produced  for  any 
reason  whatsoever. 

For  what  we  have  already  briefly  said  in  speaking  of  the 
rudder  and  elevator,  and  for  what  we  shall  say  more  dif- 
fusely in  discussing  the  problems  of  stability,  it  is  opportune 
to  know  both  of  the  coordinates  of  the  center  of  drift, 
which  define  its  position  on  the  surface  of  drift. 

Finally,  we  shall  make  brief  mention  of  the  aerodynamical 
tests  of  the  propeller. 

Let  us  suppose  that  we  have  a  propeller  model  rotating 
in  the  air  current  of  an  experimental  tunnel.  By  measur- 
ing the  thrust  T  of  the  propeller,  its  number  of  revolutions 
n,  the  power  P  absorbed  by  the  propeller,  and  the  velocity 
V  of  the  wind,  it  is  possible  to  draw  the  diagrams  of  T, 
P,  and  the  efficiency  p.  Numerous  experiments  by  Colonel 
Dorand  have  led  to  the  establis-hing  of  the  following 
relations ; 


T 

= 

a'  n 

2£)4 

P 

= 

a  n' 

.£)5 

TV 

a 

V 

p 

^^ 

P 

a 

X 

nD 

ELEMENTS  OF  AERODYNAMICS  101 

where  D  is  the  diameter  of  the  propeller,  and  a   and  a  are 
numerical   coefficients   which  vary   with   the  variation  of 

V 
—j^      This  ratio  is  proportional  to  the  other 

V     _  velocity  of  translation 
■jrnD  peripheral  velocity 

which  defines  the  angle  of  incidence  of  the  line  of  path  with 

respect  to  the  propeller  blade. 

V 
Knowing  the  values  of  a    and  a  as   functions  of  — ^' 

it  is  possible  to  obtain  those  of  T,  P,  and  p,  thereby  possess- 
ing the  data  for  the  calculation  of  the  propeller. 


CHAPTER  VIII 
THE  GLIDE 

Let  us  consider  an  airplane  of  weight  W,  of  sustaining 
surface  A,  and  of  which  the  diagrams  for  X,  8  and  the  total 
head  resistance  o-,  are  known. 

Let  us  suppose  that  the  machine  descends  through  the 
air  with  the  engine  shut  off;  that  is  gliding.  Suppose 
the  pilot  keeps  the  elevator  fixed  in  a  certain  position 
maintaining  the  ailerons  and  the  rudder  at  zero.     Then  if 

R 


Wcose 


the  airplane  is  well  balanced,  it  will  follow  a  sloping  line  of 
path  d  (Fig.  82),  which  will  make  a  well-determined  angle 
of  incidence  i,  with  the  wing;  in  fact,  if  this  angle  should 
vary,  some  restoring  couples  (see  Chapter  II),  tending  to 
keep  the  machine  at  incidence  i,  would  be  produced. 

Let  us  study  the  existing  relations  among  the  parameters 
W,  A,  X,  8,  (X,  d  and  V.  When  the  machine  has  reached  its 
normal  gliding  speed   (that  is,  V  =  constant),  the  forces 

102 


THE  GLIDE  103 

acting  on  it  are  reduced  only  to  the  weight  W,  and  the  total 
air  reaction  R.  By  a  known  theorem  of  mechanics,  all  the 
forces  acting  on  a  body  in  uniform  rectilinear  motion, 
balance  each  other;  that  is,  in  this  case  force  R  is  equal  and 
of  opposite  direction  to  W;  that  is, 

R  +  W  ^  0 
Let  us  consider  the  two  components  R^  and  R^  of  R  (on  the 
line  of  the  path  and  perpendicular  to  the  line  of  path). 
The  preceding  equation  can  then  be  divided  into  two  others 

R,  +  W  sin  0-0  (1) 

R^  +  W  cos  0  =  0  (2) 

Let  us  express  the  components  Rx  and  R^  as  function  of 
X,  5,  0-  and  7,  Remembering  what  we  have  said  in  the 
preceding  chapters, 

R^  =  10-'  XAF2 

Where  R^  is  expressed  in  lb.,  A  in  sq.  ft.,  V  in  m.p.h. 
and  X  is  a  coefficient  which  depends  upon  the  angle  of 
incidence  and  of  which  the  law  of  variation  must  be  found 
experimentally. 

As  to  i?5  its  expression  results  from  the  sum  of  two  terms, 

V 


one  due  to  the  wings  5  X  A  X  (  jr.r.  j  and  the  other  due  to 
parasite  resistances  a  of  the  form 

'  (loo)' 

Thus  we  shall  have 

R,=  10-UAV^+10-'<tV^ 
The  equations  (1)  and  (2)  become 

10-^  {bA  +  cr)   V=  -W  sine  (3) 

10-4  \AV'=  -W  cos  d  (4) 

We  have  immediately,  by  squaring   and    by  adding    the 
preceding  equations 

W  1 

10-  F^  =  ^         ,  (5) 


V(^  +  i)V 


104  AIRPLANE  DESIGN  AND  CONSTRUCTION 

and  dividing  (3)  by  (4) 

x  +  xA-'"^'  (6) 

As,  once  the  angle  of  incidence  i  is  fixed,  the  values  X  and  5 
are  fixed,  equations  (5)  and  (6)  enable  us  to  find,  cor- 
responding to  each  value  of  i,  a  couple  of  values  6  and  V. 
Thus  all  the  elements  of  the  problem  are  known. 

Equation  (5)  enables  us  to  state  the  following  general 
principles : 

1.  Other    conditions   being    equal,  the  gliding  speed  is 

W 
directly  proportional  to  the  ratio  .  '  that   is,    to   the   unit 

load  on  the  wings. 

2.  Other  conditions  being  equal,  the  gliding  speed  is 
inversely  proportional  to  the  coefficient  X ;  therefore  with 
wings  having  a  heavily  curved  surface  and  consequently  of 
great  sustaining  capacity,  the  descending  speed  is  much 
lower  than  with  wings  having  a  small  sustaining  capacity. 

3.  Other  conditions  being  equal,    the   gliding   speed  is 

inversely  proportional  to  the  value  of  sum  I  8  +    .),  which 

r> 

represents  J~  for  V  =  100  m.p.h. 

Equation  (6)  enables  us  to  state  the  following  general 
principles : 

4.  Other  conditions  being   equal,  the   angle  of   glide   9 

is  inversely  proportional  to  the  ratio  -j    that  is,  to  the 

0 

efficiency  of  the  wing. 

5.  Other  conditions  being  equal,  the  angle  of  glide  d  is 

directly  proportional  to  the  ratio  -j  between  the  coeffi- 
cient of  parasite  resistance  and  the  surface  of  the  wings. 
This  ratio  is  also  usually  called  coefficient  of  fineness. 

6.  The  angle  6  of  volplaning  is  independent  from  the 
weight  of  the  airplane.  This  weight  doesn't  influence  but 
the  speed.  In  other  words,  by  increasing  the  load,  the 
gliding  speed  will  increase  but  the  angle  of  descent  will  not 
change. 


THE  GLIDE 


105 


With  this  premise  we  propose,  following  a  method  sug- 
gested by  Eiffel,  to  draw  a  special  logarithmic  diagram  which 
will  enable  us  to  study  all  the  relations  existing  among  the 
variable  parameters  of  gliding. 

1.75   35 


1.50    30 


125    25 


1.00    20 


0.75    15 


0.50     10 


0.25      5 


1  1  1  ■  1  I  1  1  1  1  1  1  1  1  1  1  1  1  1 -           cs 

7??s 

--  ■                                                     /  ''■•' 

7 

■^K                                                    >             20 

^  '  '  *«                           Z 

^                       s^ 

i                                   -^        -.^                        175 

rrrr                       /                      N    l^            U 

i               ^/    j^  p^ 

1                 /y     i^ 

t               /   \^^ 

1              ^   ^^  ^^       '^ 

t             ^t*^      \ 

i           ^^^              s 

i      s    ^^               -  ^^ 

t               >^^                                               ^«Nl?5 

:::::::::::: ;:^^^^-:::i  -'" 

-^f---^^ 

i    ^^ 

>^                                                                      10 

J 

?d 

T/ 

lt±                                                                                                   75 

^3-2-10        1         2        3        4        5        6        7        8        9 
Degrees. 
Fig.  83. 


Let  us  go  back  to  formulas  (3)  and  (5)  and  write  them 
in  the  following  form 

-  TF  sin  0 


10-4  (3^  +  ^) 


w 


^  =  V  [10-^-  (5A  +  <r)]  ^  +  (10-4  XA)2 

Furthermore  let  us  assume 

A  =  10-4  XA 

A  =  10-4  (5A  +  (t) 


(7) 
(8) 


106 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Then  the  preceding  equations  become 
W  

-  sin  d  .  W 

72 


=  A 


(9) 
(10) 


Now,  as  for  each  value  of  the  angle  of  incidence  ^,  8,  X  and 
(T,  are  known,  and  as  A  is  constant,  we  can,  by  means  of 
equations  (7)  and  (8),  determine  a  couple  of  values  of  A 
and  A  and  consequently  of  \/a~  +  A-  and  A  corresponding 
to  each  value  of  i;  it  will  be  then  possible  to  draw  the 
logarithmic  diagram  of  \/a"^  +  A-  as  function  of  A.  A 
numerical  example  will  better  explain  this. 

Let  us  consider  an  airplane  having  the  following  charac- 
teristics : 

W  =  2700  lb. 
A  =  270  sq.  ft. 

0-  =  160  (average  value  between  i  =  0°and^  =  9°). 
X,  5  functions  of  i  as  from  the  diagram  of  Fig.  83. 
We  can  then  compile  the  following  table: 

Table  4 


i 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

X 

4.11 

6.03 

8.08 

9.70 

11.8 

13.00 

14.40 

16.10 

17.75 

19.40 

i 

0.41 

0.44 

0.45 

0.51 

0.62 

0.73 

0.89 

1.06 

1.31 

1.55 

XA 

1110 

1630 

2180 

2620 

3180 

3510 

3890 

4340 

4780 

5240 

«A+a 

271 

278 

281 

297 

327 

358 

400 

446 

514 

582 

Va2  +  A2 

0.11 

0.16 

0.22 

0.26 

0.32 

0.35 

0.39 

0.43 

0.48 

0.52 

A 

0.0271 

0.0278  0.0281 

0.0297 

0.0326 

0.0358 

0.0398 

0.0445 

0.0512 

0.0580 

Thus  we  have  a  certain  number  of  pairs  of  corresponding 
values  of  \/a^  +  A^  and  A  which  enable  us  to  draw  the 
diagram  of  Va^  +  a^  as  a  function  of  A. 

Now,  instead  of  drawing  this  diagram  on  paper  gradu- 
ated to  cartesian  coordinates,  let  us  draw  it  on  paper  with 


THE  GLIDE  107 

logarithmic  graduation  (Fig.  84).     We  shall  have  a  loga- 
rithmic diagram  which  gives 

Va'  +  A2  =  /(A) 
or 

W  _    /-TFsing\ 

Let  us  consider  any  part  whatever  of  this  curve  for  in- 
stance the  point  A;  the  abscissa  OX  of  this  point  is 

^  ^       1       —W.  sin  e 

OX  =  log y-^ 

TX''    gin  ft 

Now  log  T^^ =  log  TF  +  log  ( —  sin  0)  —  2  log  V 

Therefore  we  can  consider  OX  as  the  algebraic  sum  of  the 
segments  log  W,  log  ( —  sin  d)  and  —  2  log  V. 
Analogously  the  ordinate  of  point  A  is 

W 

w 

and  as  log  y-^    =  log  W  —  2  log  F,  we  can  consider  0  F  as 

the  algebraic  sum  of  the  two  segments  log  W  and  —  2  log  F. 

Thus  in  order  to  pass  from  the  origin  0  to  the  point  A  of 
the  diagram  it  is  sufficient  to  sum  the  segments  log  W, 
log  ( —  sin  d)  and  —  2  log  F,  following  the  axis  of  the  ab- 
scissae and  log  W  and  —  2  log  V,  following  the  axis  of  the 
ordinates. 

As  evidently,  the  segments  can  be  summed  in  any  order 
whatever,  we  can  sum  them  in  the  following  order: 

1.  Log  TF  parallel  to  OX. 

2.  Log  TF  parallel  to  OY. 

3.  -  2  log  F  parallel  to  OX. 
4.-2  log  F  parallel  to  OY. 

5.  Log  (—  sin  e)  parallel  to  OX. 

Now,  it  is  evident  that  the  two  segments  corresponding 
to  TF,  can  be  replaced  by  a  single  oblique  segment  of 
inclination  1/1  on  the  axis  OX  and  of  lengths  \/2  log  TF. 
Similarly  the  two  segments  corresponding  to  F  can   be 


108 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


replaced  by  a  single  segment  also  inclined  by  1/1  on  OX  and 
of  length  -  V2-  +  2^  log  V  Thus  we  can  pass  from  the 
origin  0  to  the  point  A  of  the  diagram  by  drawing  3  seg- 
ments, two  parallel  to  an  axis  of  inclination  1/1  on  OX  and 
one  parallel  to  OX,  and  which  measure  W,  V  and  —  sin  d 
in  the  respective  scales      The  condition  necessary  and  suf- 


0.02  A  0.03 

-0.2         Sine      -0.3 


Fig.  84. 


Q04  0.05      0.06 

-0.4  0.5     -0.6 


ficient  in  order  that  a  system  of  values  of  T7,  V  and  -  sin  B 
be  realizable  with  the  given  airplane,  is  evidently  that  the 
three  corresponding  segments,  summed  geometrically  start- 
ing from  the  origin,  end  on  the  diagram. 

The  units  of  measure  selected  for  drawing  the  diagram  of 
Fig.  84,  are  the  following: 

W  in  lb. 

y  in  m.p.h. 


THE  GLIDE  109 

In  order  to  determine  the  relation  between  the  scales 
of  Va'"^  +  A 2  and  A 2  and  the  scales  of  W,  V  and  —  sin  0, 
it  is  first  of  all  necessary  to  fix  the  origin  of  the  scale  of 
W  and  V. 

It  is  convenient  to  select  W  equal  to  the  weight  of  the 
airplane,  in  our  case  W  =  2700  lb. 

W 
Furthermore  it  is  convenient  that  the  ratio  v^  be  equal 

to  any  one  whatever  of  the  values  1  X  10^,  where  a:  is  a 

whole  positive  or  negative  number;  thus  we  have  from  the 

W 
equation  A  =  —  sin  0.  v^  that  the  same  scale  of  A,  if  divided 

by  10^,  gives  the  scale  of  —  sin  0. 

It  would  be  convenient  to  make  x  =  —  1  in  order  to 
keep  the  scale  of  —  sin  0  within  the  drawing.     Then  from 

?^  =  1  X  10-. 

We  have 

F2  =  27,000  and  V  164.3  m.p.h. 

The  scale  of  —  sin  ^  is  equal  to  that  of  A  divided  by  10"^ 
that  is,  multiplied  by  10. 

Then,  making  V  =  164.3  the  corresponding  segment  is 
zero  and  we  pass  from  the  origin  0  to  a  point  of  the  diagram 
by  summing  geometrically  the  segments  corresponding  to 
—  sin  6  and  W.  Let  us  consider  any  point  whatsoever  B 
of  the  diagram,  for  instance  the  point  whose  coordinates  are : 


Va-  +  A^  =  0.3  and  A  =  0.031 

For  this  point  and  for  V  =  164.3,  the  weight  W  is  repre- 
sented by  the  segment  BB' ;  because 

W 


V  A^     +     A^  y^ 


substituting  the  preceding  values  of  \/a^  +  A-  and  V,  we 
have 

W  =  8100 
that  is  BB'  =  8100 


no 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Let  US  make  now  W  =  2700;  then  the  corresponding 
segment  is  zero  and  in  order  to  pass  from  the  origin  0  to 
a  point  of  the  diagram  it  would  be  sufficient  to  sum  geo- 
metrically the  segment  corresponding  to  —  sin  6  and  V. 
Let  us  take  any  other  point  whatsoever  C  on  the  diagram, 
for  instance  that  whose  coordinates  are: 

\/a^+-^-  =  0-2  and  A  =  0.0278 
For  this  point  and  for  W  =  2700  we  shall  have,  as  it  is 
demonstrated  with  an  analogous  process,  that  CC  =  F  = 
116.3  m.p.h. 


Sin  e  =   010 


Fig.  85. 

Taking  BB'  to  O'B"  on  the  scale  of  W  and  marking 
2700  lb.  in  0'  and  8100  lb.  in  B" ,  the  scale  of  weights  will 
be  individuated.  Analogously  taking  CC  to  0"C"  on  the 
scale  of  V  and  marking  164.3  on  0"  and  116.3  on  C",  the 
scales  of  speed  will  be  individuated. 

With  the  preceding  scales  and  for  the  airplane  of  our 
example  weighing  2700  lb.,  the  diagram  of  Fig.  84  gives 
immediately  the  pair  of  corresponding  values  of  —  sin  d 
and  V.  In  fact  for  any  value  whatsoever  of  —  sin  d  for 
instance,  from  the  point  C  correspondent  to  —  sin  ^  = 
0.139,  it  is  sufficient  to  draw  a  parallel  to  the  scale  of 
speeds  until  it  meets  the  diagram  in  C;  the  segment  CC, 
read  on  the  scale  of  the  speeds  gives  the  value  of  the  speed 
V  corresponding  to  —  sin  0;  in  our  case  CC  =  116.3. 
From  the  diagram  we  see  that  by  increasing  the  angle  of 
incidence,  the  angle  6  decreases  to  a  minimum,  after  which 
it  increases  again.  This  means  that  the  line  of  path  raises 
its  inclination  up  to  a  limit  which  in  our  case  is  equal  to 


THE  GLIDE  111 

about  0.1  corresponding  to  the  incidence  of  5°  to  6°;  if  our 
airplane  was  descending  for  instance  from  the  height  of 
1000  ft.  it  could  reach  any  point  whatsoever,  situated  within 
a  radius  of  9950  ft.  (Fig.  85). 

Our  example,  however,  is  referred  to  an  exceptional  case ; 
in  practice  with  the  present  airplanes,  the  minimum  value 
of  sin  d  is  between  0.12  and  0.14.  Furthermore  the  dia- 
gram shows  the  law  variation  of  the  speed  of  the  airplane 
with  a  variation  of  the  angle  of  incidence.  It  is  seen  that 
it  is  not  safe  to  decrease  too  much  the  angle  of  incidence 
in  order  not  to  increase  excessively  the  speed. 

In  practice  the  pilots  usually  dispose  the  machine  even 
vertical  but  for  a  very  short  time,  so  as  not  to  give  time  to 
the  airplane  to  reach  dangerous  speeds.  On  the  other  hand 
one  has  to  look  out  not  to  increasing  excessively  the  angle 
of  incidence  in  order  not  to  fall  in  the  opposite  incon- 
venience of  reducing  excessively  the  speed,  which  causes 
a  strong  decrease  in  the  sensibility  of  the  controlling 
devices  and  consequently  in  the  control  of  the  machine 
by  the  pilot. 

The  use  of  speedometers,  today  much  diffused,  is  a  very 
good  caution  in  order  that  the  pilot,  while  gliding  may 
keep  the  speed  within  normal  limits,  keeping  it  preferably 
slightly  below  the  normal  speed  which  the  machine  has  with 
engine  running. 

Until  now  we  have  treated  the  rectilinear  glide.  It  is 
necessary  to  take  up  also  the  spiral  glide  which  is  today  the 
normal  maneuver  for  the  descent. 

The  spiral  descent  is  accomplished  by  keeping  the 
machine  turning  during  the  glide.  We  have  seen  that  a 
centrifugal  force  is  then  originated 

W    V 


equal  and  opposite  to  the  centripetal  force  R\  which  has 
provoked  the  turning  (Fig.  86).  This  force  R's  can  be  pro- 
duced by  the  inclination  of  the  airplane  or  by  the  drifting 
course  of  the  airplane  or  by  both  phenomena.     When  this 


112  AIRPLANE  DESIGN  AND  CONSTRUCTION 


V 


^^. 


V 


FiQ.  86. 


THE  GLIDE  113 

force  is  provoked  solely  by  the  inclination  of  the  airplane, 
that  is,  when  the  angle  of  drift  is  zero,  we  say  the  spiral 
descent  is  correct,  the  machine  then  doesn't  turn  flat; 
as  in  practice  this  is  the  normal  case,  we  shall  study  only 
this  case.  We  developed  the  discussion  for  this  case  as  if 
the  weight  were  increased  from  W  to  W  where 

COS  a 

Therefore  we  can  apply  the  formulae  of  the  rectilinear 
gliding,  but  we  shall  be  careful  to  consider  the  angle  d' 
of  the  line  of  path,  with  a  plane  perpendicular  to  W 
instead  of  the  angle  0  of  the  line  of  path  with  the  horizontal ; 
in  fact,  as  we  consider  the  fictitious  weight  W  instead  of  the 
weight  TF,  we  shall  have  to  consider  a  fictitious  horizontal 
plane  perpendicular  to  W  instead  of  the  horizontal  plane 
perpendicular  to  W. 

Then  equations  (3)  and  (4)  become 

10-^  {bA  +  a)F2  =  -^^  sin  d'  (11) 

cos  a 

10-^  \AV^  =  ^^  COS  d'  (12) 


from  which 
10- 

{dA  +<t)V' 


-^^  =  %/J^X»+(,  +  ^)^Vcos 


sin  d'  =  10-^ 


W 

If  we  make  a  =  0,  we  have  cos  a  =  I,  and  we  fall  back  to 
the  formula  for  rectilinear  gliding. 

Calling  Vo  and  do  the  values  of  V  and  6  for  a  =  0,  and 
calling    V„   and  d'^  the  values  for  the  angle  a,  we  have 


Vcos  a 

sin  d'„  =  sin  do 
From  known  theorems  of  geometry,  calling  6^  the  angle 
of  the  line  of  path  with  the  horizontal,  we  have 
sin  d'    =  sin  6^  .  cos  a 


114  AIRPLANE  DESIGN  AND  CONSTRUCTION 

from  which 

sin  do    ' 
sin  d„  = 

cos  a 

Resuming,  if  we  suppose  that  we  maintain  a  certain  incidence 
?■  (by  maneuvering  the  elevator)  and  a  certain  transverse 
incUnation  a  (by  maneuvering  the  ailerons)  the  airplane 
will  follow  an  elicoidal  line  of  path,  with  speed  F„  and 
inclination  to  the  ground  ^„  which  are  given  by  the  equations: 

F„  =  — ^  (13) 

V  cos  a 

and 

•     n        sin  do  /I.N 

sm  d„  =  (14) 

cos  a 

where  Vo  and  do  are  the  speed  and  the  inclination  of  line  of 
path,  corresponding  to  the  rectilinear  gliding;  it  is  then 
easy,  from  diagram  84,  to  obtain  the  couples  of  values  V„ 
and  sin  d„  corresponding  to  each  value  of  a. 

In  general,  equations  (13)  and  (14)  tell  us  that  in  the 
spiral  descent  the  angle  of  incidence  being  kept  the  same, 
an  airplane  has  a  speed  and  an  angle  of  slope  of  the  line  of 
path  which  are -greater  than  in  the  rectilinear  gliding. 


CHAPTER  IX 

FLYING  WITH  POWER  ON 

In  the  preceding  chapter  we  have  studied  gliding  or 
flying  with  the  engine  off.  Let  us  suppose  now,  that  the 
pilot,  during  any  course  whatever  of  gliding,  starts  the 
engine  without  maneuvering  the  elevator.     Then  a  new 


force  will  appear,  other  than  the  weight  W  and  air  reaction 
R,  namely,  the  propeller  thrust,  T. 

If,  instead  of  weight  W,  we  consider  the  fictitious  weight 
W  resulting  from  TT^  and  T  (Fig.  87),  all  the  considerations 
made   and   notations   adopted   in   the   preceding   chapter 
can   be   applied. 
Then 

R,  =  T  +  W  cos  (90°-^)  =  r  +  IF  sin  ^ 

7?x  =  ^T^  cos  d 

115 


116  AIRPLANE  DESIGN  AND  CONSTRUCTION 

or 

10-"  {8 A  +<t)V'  =  T  +  W  sin  d  (1) 

10-'\AV^  ==  W  cose  (2) 

Eliminating  10"^  F^  from  the  two  equations,  we  have 

(5A  +  cr)  .  K^ll  =  r  +  TF  sin 
from  which 

T  =  (^-  +  ^Wcosd  -W  sin  e  (3) 

Let  us  suppose  that  the  angle  of  incidence  is  fixed,  then 
X,  5,  and  a,  will  be  determined.  Equation  (3)  enables  us  to 
find  the  value  of  6  for  each  value  of  T.  For  7"  =  0,  we 
return  to  the  case  of  gliding.  As  T  increases,  cos  6  must 
increase,  and  sin  6  must  decrease;  that  is,  the  angle  6 
decreases.  Value  To,  for  which  d  =  0,  gives  the  value 
of  thrust  necessary  for  horizontal  flight.  For  6  =  0,  we 
have  cos  ^  =  1,  and  sin  0  =  0;  consequently 


{j  +  Ia)x^  (^) 


for  all  the  values  T  <  To,  the  angle  6  with  the  horizontal 
line  is  positive;  that  is,  the  machine  descends.  For  all  the 
values  T>To,  the  angle  6  with  the  horizontal  line  changes 
sign;  that  is,  the  line  of  path  ascends.  First  of  all  let  us 
study  horizontal  flight.  Then,  as  0  =  0  equation  (1)  and  (2) 
become 

T  =  10-''  {8A  +  <r)  72  (4) 

W  =  10-"  \AV'  (5) 

Now  the  power  Pi  in  H.P.  corresponding  to  the  thrust  T  in 
lb.  and  to  the  speed  V  in  m.p.h.,  it  is  evidently  equal  to 

=  1A7TV 
and  because  of  equation  (4) 

55OP1  =  1.47  10-"  {6A  +  <r)  73  (6) 


FLYING  WITH  POWER  ON 


117 


Equations  (5)  and  (6)  enable  us  to  draw  a  very  interesting 
logarithmic  diagram  with  the  method  proposed  by  Eiffel. 
Let  us  have  as  in  the  preceding  chapter 

A  =  10--^  \A 

A  =  10-4  (5A  +  a) 

Equations  (5)  and  (6)  become 
550Pi 


A 


(7) 


=  1.47  A 


(8) 


Let  us  consider  then  the  airplane  of  the  example  used  in  the 
preceding  chapter,  that  is,  the  airplane  having  the  following 
characteristics: 

W  =  2700  lb. 

A  =  270  sq.  ft. 

(X    =  160 

and  whose  diagrams  of  \  and  5  are  those  given  in  Fig.  83. 
Based  upon  the  table  given  in  the  preceding  chapter  we  can 
compile  the  following  table : 

Table  5 


0.11      0   16      0.2: 


0.26      0.32      0.35     lO. 


1.47  A  0.0398,0.0410  0.0413  0.0437  0.0480  0.0527  0.0587  0.0655  0.0755 

I  I  ■  III 


0.52 
0.0853 


This  table  gives  a  certain  number  of  pairs  of  values  cor- 
responding to  A  and  A  and  therefore  enables  us  to  draw  the 
diagram  of  A  as  as  function  of  A.  Now  instead  of  drawing 
(he  diagram  on  paper  graduated  with  uniform  scales,  let  us 
draw  the  same  diagram  on  paper  with  logarithmic  graduation 
(Fig.  88). 

We  shall  have    a  logarithmic  diagram  which  gives 

A=/(1.47A) 


W^ 

V^ 


I 


550Pi 


iOPA 
73   j 


118  AIRPLANE  DESIGN  AND  CONSTRUCTION 

■>< 


8  I 


FLYING  WITH  POWER  ON  119 

Let  us  consider  then  any  point  whatever  of  this  curve 
for  instance  the  point  A ;  the  abscissa  OX  of  this  point  is 

OX  =  log  — p^ 

550P 
Now  log     Tr3     "^  log  55OP1  —  3  log  V;  thus  we  can  con- 
sider  OX   as   the   algebraic   sum  of   segment   log   550Pi, 
and  segment  —3  log  V.     Analogously  the  ordinate  of  point 
A  is 

W 
OY  =  log  ^2 

W 

and  as  log  ^"2  =  log  TF  —  2  log  V  we  can  consider  OF  as 

the  algebraic  sum  of  the  two  segments  log  W  and  —2  log 
V.  Thus,  in  order  to  pass  from  the  origin  0  to  point  A  of 
the  diagram,  it  is  sufficient  to  add  the  segment  log  550 
Pi  and  —3  log  V  along  the  axes  OX  and  log  W  and  —2 
log  V  along  the  axes  OY. 

Since  evidently  these  segments  can  be  added  in  any 
order  whatever,  we  can  take  first  log  550Pi  parallel  to  the 
axes  of  abscissa,  then  —3  log  V  also  parallel  to  the  axes 
of  abscissa,  then  —  2  log  V  parallel  to  the  axes  of  ordinates 
and  finally  log  TF  parallel  to  the  axes  of  ordinates. 

Now  it  is  evident  that  the  two  segments  —3  log  V  and 
—  2  log  V  corresponding  to  V,  can  be  replaced  by  a  single 
oblique  segment  whose  inclination  is  2  on  3  and  w^hose  length 
is  —  \/2^  +  3^  .  log  V.  Thus  we  can  pass  from  the  origin 
0  to  point  A  by  drawing  three  segments,  one  parallel  to  the 
axes  OX,  the  second  parallel  to  an  axes  of  an  inclination  of 
2  on  3  and  the  third  parallel  to  the  axes  OY  which  segments 
measure  in  the  respective  scales  Pi,  V  and  W. 

The  condition  necessary  and  sufficient  in  order  that  a 
system  of  values  of  Pi,  V  and  W,  may  be  realized  with  the 
given  airplane  is  evidently  that  the  three  corresponding 
segments,  summed  geometrically  starting  from  the  origin, 
end  on  the  diagram. 


120  AIRPLANE  DESIGN  AND  CONSTRUCTION 

The  units  of  measure  selected  for  drawing  the  diagram 
of  Fig.  88  are  the  following: 

Pi  in  H.P. 
V  in  m.p.h. 
W  in  lb. 

In  order  to  determine  the  relation  between  the  scales 
of  A  and  A  and  the  scales  of  Pi,  V  and  W,  it  is  necessary 
to  fix  the  origin  of  the  scale  of  V;  we  shall  suppose  to 
assume  as  origin  V  =  100  m.p.h.  Then  for  V  =  100  m.p.h., 
the  coordinates  A  and  A  measure  also  W  and  P;  in  fact  for 
the  particular  value  V  =  100  the  segment  to  be  laid  off 
parallel  to  the  scale  of  V  becomes  zero  and  so  we  go  from  the 
origin  to  the  diagram  through  the  sum  of  the  only  two  seg- 
ments W  and  P.  Let  us  consider  then  the  point  A  whose 
coordinates  are 

A  =  0.3  and  A  =  0.0463 
Corresponding  to  these  points  we  shall  have 

which  gives 

W  =  3000  lb.        Pi  =  84.2  H.P. 

Thus  the  scales  of  W  and  Pi  are  determined. 

In  order  to  determine  the  scale  of  V  we  proceed  as  follows: 
Let  us  give  to  W  and  Pi  two  values  whatever,  for  instance 

W  =  3000  and  Pi  =  200  H.P. 

Applying  the  usual  construction  we  shall  lay  off  OB  = 
3000,   BC  =  200  in  the  respective  scales;  from  point  C 
we  draw  a  parallel  to  the  scale  V  to  meet  the  diagram  in 
point  D.     We  shall  have  in  CD  the  corresponding  speed. 
Now  for  point  D   A  =  0.153.     Consequently,  as  we  have 

0.153  =  ?^ 

we  will  have 

V  =  140  m.p.h, 


FLYING  WITH  POWER  ON  121 

that  is,  the  segment  CD  laid  off  in  0"D'  gives  the  scale  of 
V.  The  scales  being  known  it  is  easy  to  study  the  way  the 
airplane  acts,  that  is,  it  is  possible  to  find  for  each  value 
of  the  speed  the  value  of  the  power  necessary  to  fly. 

In  Fig.  88  we  have  disposed  the  scales  so  as  to  facilitate 
the  readings;  that  is  we  have  made  the  origin  0"  of  the  scale 
of  V  coincide  with  the  intersection  of  this  scale  and  a  Une 
O'X'  parallel  to  the  axis  OX  and  passing  through  the  value 
W  =  2700  which  is  the  weight  of  the  airplane;  and  we  have 
furthermore  repeated  on  O'X'  the  scale  of  power. 

Then,  in  order  to  have  two  corresponding  values  of  P  and 
V  we  draw  from  any  point  whatever  E  on  the  scale  of  the 
speed,  the  parallel  to  OX  up  to  F,  point  of  intersection  with 
the  diagram;  we  draw  then  FF'  parallel  to  the  scale  of  the 
speed  and  we  have  in  F'  on  O'X'  the  value  of  the  power 
Pi  corresponding  to  a  speed  E.  The  examination  of  the 
diagram  enables  us  to  make  some  interesting  observations. 

Let  us  draw  first  the  tangent  t  to  the  diagram  which  is 
parallel  to  scale  V;  this  tangent  will  cut  the  axis  O'X' 
in  a  point  corresponding  to  a  power  of  58  H.P. ;  this  is  the 
minimum  power  at  which  the  airplane  can  sustain  itself 
and  the  corresponding  speed  Fmin  is  72.3  m.p.h. 

An  airplane  having  an  engine  capable  of  giving  no  more 
than  this  power,  could  hardly  sustain  itself;  it  would  be, 
as  one  says,  tangent,  and  could  only  fly  horizontally  or  de- 
scend, but  could  by  no  means  follow  an  ascending  line  of 
flight. 

For  all  the  values  of  speed  greater  or  lower  than  the 
above  value,  the  necessary  power  for  flying  increases.  The 
phenomenon  of  power  increasing  for  the  decreasing  speed 
may  seem  strange ;  even  more  so,  if  the  comparison  is  made 
with  all  other  means  of  locomotion,  for  which  the  necessary 
power  for  motion  is  so  much  greater  as  the  speed  of  motion 
increases.  But  we  must  reflect  that  in  the  airplane,  the 
power  necessary  for  motion  is  partly  absorbed  in  overcom- 
ing the  passive  resistances,  partially  in  order  to  insure 
sustentation ;  this  dynamical  sustentation  admits  a  maxi- 


122  AIRPLANE  DESIGN  AND  CONSTRUCTION 

mum  efficiency  corresponding  to  a  given  value  of  speed, 
below  which,  consequently,  the  efficiency  itself  decreases. 

Practically,  the  speed  Fn,in  corresponds  to  the  minimum 
value  which  the  speed  of  the  airplane  can  assume.  It  is 
quite  true  that  theoretically  the  speed  of  the  airplane  can 
still  decrease,  but  the  further  decrease  is  of  no  interest,  as 
it  requires  increase  of  power  which  makes  the  sustentation 
more  difficult,  and  therefore  the  flight  more  dangerous. 

When  the  speed  increases  to  values  greater  than  Fmin; 
the  power  necessary  for  sustentation  rapidly  increases. 
The  maximum  value  the  airplane  speed  can  assume, 
evidently  depends  upon  the  maximum  value  of  useful  power 
the  propeller  can  furnish. 

Let  P2  be  the  power  of  the  engine,  and  p  the  propeller 
efficiency;  the  useful  power  furnished  by  the  propeller  is 
evidently  pP2- 

To  study  flying  with  the  engine  running,  it  is  necessary 
to  draw  the  diagram  pP2  as  a  function  of  V,  in  order  to  be 
able  to  compare  for  each  value  of  V,  the  power  pP2  available 
for  that  speed,  and  the  power  necessary  for  flying,  also  at 
that  speed. 

Therefore,  it  is  necessary  to  know  the  following  diagrams : 

(1)  P,=f  (n) 

(2)  a  =  f  I  ^^  ] ,  which  gives  the  value  of  coefficient  a 

of  the  formula  Pp  =  anW^,  corresponding  to  the  power 
absorbed  by  the  propeller,  and 

The  first  of  the  three  diagrams  must  be  determined  in 
the  engine  testing  room,  and  the  other  two  in  the  aerody- 
namical laboratory.  When  they  are  known,  the  determi- 
nation of  values  pP2  as  a  function  of  V  becomes  possible 
by  using  a  method  also  proposed  by  Eifell,  and  which 
is  interesting  to  expose  diffusely. 


FLYING  WITH  POWER  ON  123 


Let  US  consider  the  equation 

Pp  =  anW> 
or 


n^D' 


As  we  have  seen  in  chapter  6,  a  =  •^("n)'  ^-herefore 

n'  D'      ''  \nD/ 

Now,  instead  of  drawing  the  diagram  by  taking  the  values 

V  Pp  .  . 

of  — T<  as  abscissae,  and  those  of  -^t^^,  as  ordinates  on  uni- 
nD  n^D-" 

form   scales,    let   us   take    these   values,    respectively,    as 

abscissae   and   as    ordinates,    on   paper    with    logarithmic 

graduation    (Fig.   89). 

P  /  V  \ 

Let  us  now  consider  a  point  on  the  curve  ^  w^  =  /(  --^  ) ; 

for  instance,  point  A.     The  abscissa  of  this  point  is  OX  = 

V  V 

log  —j^;  but  log  -j<  =  log  V  —  log  n  —  log  D,  conse- 
quently we  can  consider  OX  as  the  algebraical  sum  of  the 

following  three,  log  V,  —  log  n,  and  —  log  D.     Analogously, 

p 
the  ordinate  07  of  point   A,  is   07  =  log  -^£^'  and  we 

can  write  07  =  log  Pp  —  3  log  n  —  5  log  D,  considering 
07  as  the  algebraic  sum  of  the  following,  log  P,  —  3  log  n 
and  —  5  log  D.  Then,  in  order  to  pass  from  the  origin  0, 
to  point  A  of  the  diagram,  it  is  sufficient  to  add  log  V,  — 
log  n  and  —  log  D  following  axis  OX,  and  log  Pp,  —  3 
log  n  and  —  5  log  D  following  axis  OY. 

Since  evidently  these  segments  can  be  added  in  any  order 
whatever,  we  can  first  take  log  V,  then  —  log  n  parallel  to 
axis  OX,  and  —  3  log  n  parallel  to  the  axis  of  the  ordinates, 
then  again  —  log  D  parallel  to  the  axis  of  the  abscissae,  and 
—  5  log  D  parallel  to  the  axis  of  the  ordinates,  and  finally 
log  Pp.  Now  it  is  evident  that  the  two  segments  —  log  n 
and  —  3  log  n  corresponding  to  n,  can  be  replaced  by  a  sin- 
gle oblique  segment  with  an  inclination  of  3  on  1  and  having 


124 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


a  length  proportional  to  log    n.     Analogously,    the    two 
segments  —  log  D   and  —  5  log  D   corresponding    to    D, 


SCALE  D 


A50 

i 

4"-"o 

~    "Tvi^^ 

,   1/  s      /              ^ 

'^J/ 



ZL 



II 

n 

— 

F'T"" 

z 

■300 

aoxio^ 

— 

— 

— 

= 

= 

- 

/Tf'^ 

S 

•^ 

4              A 

f 

'^^W 

-= 

- 

— 

= 

- 

- 

/- 

f^V"- 

- 

u 

■it" 

-zsoLaxio"^ 

.150 

9 

as 

= 

E 

E 

E 

E 

—  ---^ 

=: 

z. 

...^. 

:_.:^ 

— 

— 

— 

— 

ATI     f- 

Z--SS 

5" 

, 

1  _ 

n 

t 

-   '--  X, 

^ 

'/ 

1    ~ 

1 

* 

l7 

tZc 

j 

17 

1 

t 

j 

/ 

j 

] 

/ 

^/^M." 

1 

'.T 

/ 

s    1 

t-t^ 

1 

1 

i 

] 

r 

~1 

~r 

::r: 

1 

1 

mtttr 

1 

^     m 

0.6 

-100      0.7 

-90  Pp 

HP06 
•80 

■70       0.5 

•60 

0 
•50 

E 

m 

1 

E 

_  t. 

—  H-^ 

^ 

^ 

,.i 

— 

'— 

— 

-^n : 

-::;?!'- 

— 

^  ?!   ^     — , 

"^r       V 

~i 

^^ 

I 

>  '^ 

Hj    -jo. 

„ 

1 

ji:'^ 

1 

f 

j 

/ 

y  / 

/ 

r 

7 

/ 

/ 

/ 

/ 

L 

/      , 

-.11     I 

4C 

-^         4x10'^        5x10'^      6x10 
50          60          70        80 

■^    7x10^  &xl0'^9xl0"^0xl0'^    12x10 
90      100                            150 

-3    14x10-' 
200 

V.m.p.h. 
Fig.  89. 

can  be  replaced  by  a  single  oblique  segment  with  inclina- 
tion of  5  on  1  and  having  a  length  proportional  to  log  D. 

We  can  definitely  pass  from  origin  0  to  point  A  of  the 
diagram,  by  drawing  four  segments  parallel  respectively  to 


FLYING  WITH  POWER  ON  125 

axis  ox,  to  an  axis  of  inclination  3  on  1,  to  an  axis  of  inclina- 
tion 5  on  1,  and  to  axis  OY,  and  which  measure  V,  n,  D,  and 
Pp,  in  their  respective  scales. 

The  condition  necessary  and  sufficient  for  a  system  of 
values  of  V,  n,  D  and  Pp  to  be  realizable  with  a  propeller 
corresponding  to  the  diagram,  is  evidently  that  the  four 
corresponding  segments  (added  geometrically  starting  from 
the  origin)  terminate  on  the  diagram. 

The  units  of  measure  selected  for  drawing  the  diagram  of 
Fig.    89   are: 

V,  in  miles  per  hour 

n,  in  revolutions  per  minute 

D,  in  feet  and 

PpinH.P. 

In  order  to  determine  the  relation   between  the   scales 

V  P 

of  — ^  and  -T^  and  those  of  V,  Pp,  n,  and  D,  it  is  neces- 

sary  to  fix  the  origin  of  the  scales  of  n  and  D.     Let  us 

suppose  that  the  origin  of  the  scale  n  be  1800  r.p.m.  and  that 

of  scale  D  be  7.5  ft.     Then  for  n  =  1800  and  D  =  7.5  the 

V  P 

coordinates  — ^  and  ~jfjb  evidently  also  measure  V  and 

Pp-,  in  fact  for  these  particular  values,  the  segments  to  be 
laid  off  parallel  to  the  scales  n  and  D,  become  zero,  and  so 
we  go  from  origin  to  the  diagram  by  means  of  the  sum  of 
only  the  two  segments  V  and  Pp.  Then,  considering  for 
instance  the  speed  V  =  100  m.p.h.,  it  must  be  marked  on 

the  axis  OX  at  the  point  where  ^  =  .,  onn  v^  t  g  =  0.0074. 
^  nD       1800  X  7.5 

In  this  way  the  scale  of  V  is  determined. 

Corresponding  to  F  =  100  m.p.h.  we  have  (see  diagram 
p 
Fig.  89)  ^^  =  2.46  X  lO-^^.  thus,  making  n  =  1800  and 

D  =  7.5  we  shall  have  Pp  =  340  H.P. ;  marking  the  value  of 

p 
P  =  340  in  correspondence  to  -yg^  =  2.46  X  lO-^^  deter- 
mines the  scale  of  powers  Pp. 

In  order  to  find  the  scale  of  D,  make  n  equal  to  1800, 
for  which  the  segment  n  is  equal  to  zero. 


126  AIRPLANE  DESIGN  AND  CONSTRUCTION 

Now,   by   giving   V  and  Pp  any  two  values  whatever 

(for   instance    V  =  100   m.p.h.   and  Pj,  =   100   H.P.)    by 

means  of  the  usual  construction  a  segment  BC  is  determined, 

which  measures  the  diameter  D  on  the  scale  of  D.     The 

p 
value  of  D  results  from  the  value    ,J!,.'  which  is  read  on  the 

diagram  at  point  C;  in  our  case,  this  value  is  2.22  X  lO"*'^ 
and  consequently,  as  Pp  =  100  and  n  =  1800,  we  shall 
have 

1800«  X  D' 

which  gives  D  =  6  ft.     Thus,  by  taking  to  the  scale  of  D, 

starting  from  origin  0'  (which  is  supposed  to  correspond 

to  D  =  7.50  ft.),  a  segment  O'D'  =  BC,  and  marking  the 

value  6  ft.  on  the  point  D',  the  scale  of  D  is  obtained. 

Finally,  to  find  the  scale  of  n,  it  is  sufficient  to  make  D  = 

7.5,    V  =  100   m.p.h.    and  Pp  =  100,    and   by    repeating 

analogous    construction   we   find   that   the   segment   BC 
p 

corresponding  to  C  is  ^^  =  2.06;  then  for  Pp  =  100  and 

D  =  7.5  the  result  is  n  =  1270.  Then,  by  taking  to  the 
scale  of  n,  starting  from  origin  0"  (which  by  hypothesis  is 
equal  to  n  =  1800),  a  segment  0"D"  =  BC,  and  marking 
the  value  1270  r.p.m.  on  the  point  D",  the  scale  of  n  is 
defined. 

Analogously,  we  can  also  draw  the  diagram  p  =  f[~Tj)' 

on  the  logarithmic  paper,  by  selecting  the  same  units  of 
measure  (Fig.  89), 

Let  us  suppose  that  we  know  the  diagram  Pi  =  f  (n), 
(Fig.  90),  which  is  easily  determined  in  the  engine  testing 
room;  we  can  then  draw  that  diagram  by  means  of  the 
scale  n,  and  the  scale  of  the  power  shown  in  Fig.  89 
(Fig.  91). 

Disposing  of  the  three  diagrams 

n'D''      '  \nDJ 


=  '© 


P2  =  /  in) 


FLYING  WITH  POWER  ON 


127 


drawn  on  logarithmic  paper,  it  is  easy  to  find  the  values 
pPi  corresponding  to  the  values  of  V. 

In  fact  let  us  draw  in  Fig.  91,  starting  from  the  origin 
of  the  scale  of  n,  a-  segment  equal  to  diameter  D  of  the 
propeller  adopted,  measuring  D  to  the  logarithmic  scale 
of  Fig.  89,  in  magnitude  and  direction.     We   shall  have 


?oo, 


^ 

^y^ 

y 

^^ 

y 

y 

/^ 

/_ 

-^^,4 

J^ 

AU 

^T 

1 

7 

/ 

t 

t 

7 

f 

J 

1400 


l&OO 
n 
Fig.  90. 


point  F';  then  draw  the  horizontal  line  Y'x.  Supposing 
that  Fig.  91  be  drawn  on  transparent  paper,  let  us  take 
it  to  the  diagram  of  Fig.  89,  making  Vx  coincide  with 
axis  OX,  and  the  point  Y'  with  any  value  Y  whatever,  of 
the  speed. 

Fig.  92  shows  how  the  operation  is  accomplished,  suppos- 
ing Y'  to  be  made  coincident  with  Y  =  100  m.p.h.  and 
supposing  Z)  =  9.0  feet. 

The  point  of  intersection  A  between  the  curves  Pj,  and 


128 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


-500 
^450 
-400 
-350 
-300 

-250 
-200 

-150 


■100 


FLYING  WITH  POWER  ON 


129 


:500 
450 

-400 
350 

■300 
250 

■eoo 

150 


•100 


^50 


i 

Pp. 

Q9 
08 
07 
0.6 

0.5 

0 

r/ 

A 

/ 

1 

/             > 

aV^/ 

/I 

V       \ 

mo 

w'l 

mo            X 

\J'<00 

Jpoo 
ci  mo 

fa 
/     ' 

I I L. 


40        50      60     TO    50   90  100 

Fig.  92. 


150         200 


130  AIRPLANE  DESIGN  AND  CONSTRUCTION 

P-i  determines  the  values  of  Po,  p  and  rt  corresponding  to  an 
even  speed.  ^ 

We  can  then  determine  for  each  value  of  V,  the  corre- 
sponding value  Pn,  and  we  can  obtain  the  values  p  X  P2 
corresponding  to  those  of  V  in  Fig.  88.  This  has  been  done 
in  Fig.  93.  Comparing,  in  this  figure,  the  values  of  pPi  and 
Pi  corresponding  to  the  various  speeds,  we  see  that  pP^  = 
Pi  for  V  =  160  m.p.h. ;  this  value  represents  the  maximum 
speed  that  the  airplane  under  consideration  can  attain; 
in  fact  for  higher  values  of  V,  a  greater  power  to  the  one 
effectively  developed  by  the  engine  at  that  speed,  would  be 
required. 

For  all  the  speed  values  lower  than  the  maximum  value 

V  =  160  m.p.h.  the  disposable  power  on  the  propeller  shaft 
is  greater  than  the  minimum  power  necessary  for  horizontal 
flight;  the  excess  of  power  measured  by  the  difference  be- 
tween the  values  pP2  and  Pi,  as  they  are  read  on  the  loga- 
rithmic scales,  can  be  used  for  climbing.     The  climbing  speed 

V  is  easily  found  when  the  weight  TT^  of  the  machine  is  known. 
In  fact  in  order  to  raise  a  weight  W  at  a  speed  v,  a  power  of 

vXW  lb.  ft.  =  ^^  X  V  X  W  H.P.  is  necessary;  we  now 

dispose  of  a  power  pPi  —  Pi,  consequently  the  climbing 
speed  is  given  by 

"^^  -  ^'  =  550  ^  "  >^  '^ 


that  is, 


t'  =  ^  X  (pp,  -  Pi: 


The  climbing  speed  is  thus  proportional  to  the  difference 
pP2  —  Pi;  it  will  be  maximum  corresponding  to  the  maxi- 
mum value  of  pP2  —  Pi;  in  our  example,  this  maximum 
is  found  for  V  =  95  and  corresponding  to  it  i;  =  33  ft. 
per  sec. 

'  In  fact,  point  A  determines  a  pair  of  values  of  V  and  n,  which  are  com- 
patible either  to  the  diagram  of  the  power  absorbed  by  the  propeller,  or  to 
the  diagram  of  the  power  developed  by  the  engine. 


FLYING  WITH  POWER  ON 
X 


131 


Tx:  — 

■ :.::: ^  o 

_                                    o 

X  ^ 

—  -    -             s 

g 

■•"%  "  -     ' 

o_ 

\                                          '--' 

^ 

'                                                 5 ! 

;::  ;:;i;::|;;;:;:;::::::::i 

- S     - 

H^'^M^i  ^jfJ      1 1 

Tin     °1 

"= .  .Jk-^-J^iJ    a  Ml 

^ 

V — -s  --- 

\ 

s 

\       o 

^  ^-r "1 hsX-S 

V  <2'  + 

<,\  ^ 

K     1 "h^UZ 

\                       ■  'i 

>N :::::::::::::is 

o 

'i                                     -R  ^ 

CJ 

s S  ^vJi 

:   :::::v::t::::::::::::::::  .^S 

t::::::::::  =  . ^. ::=-=--  S        - 

::  i;;::::::ft:!;=E=;nln^ 

H^l          1      k  - 

^h|||||||iI44tI  '^^ 

■''S 

|::i^:--::iiE=;EEEn-- 

1  1  nJ      m^^ 

+11 1 '  -^ 

ai:i::s-::::::::-: : 

:    ::::'.::\,(^ _            trj^cc 

■■•■  +  ■•    Ml'    TV  1  t  !  1    ■  ^      1  '  1 

l^o         V6'                              L 

:_:::::::::::s±-: g  ^ 

Bi#^^#sp 

'rnti^^ 

|§HbJ4i,itfcHW.H  :T1iinT 

I^IiI^^Ieeee 

-V ^---  e^^-°cu 

r:;;:;::::::::$z:i-^=^ 

,^. ::::::::::::::   :                $ 

s;-g  -\ 

-                        V 

.  1      "  " 

V    "" _                s 

is;::::    :::  :                    "^ 

"     A  •?>  --      - 

.     JV"^  -     - 

7\^ 

:   :^s::::::___  _             q 

\                           ^ 

-       -      -             -,f 

ly 

i ..iinig-.- — I]: 

:  :::::::v%Ti:::  :- 

g##^S==^======t===== 

1  1     1  1 1 1 N| 1  1  1  1  1  II  1  1  ■ 

:-:::::::::::\  OL 

.     \>^  - 

-  a  \ 

::._____        s  n 

yi^D.  . 

y-'. 

V| 

"      Itl              o 

-    ---               -fs;;;          g 

1  1 

_^_^  o 

°  <: 


iSigsi  i  I  §  = 


132  AIRPLANE  DESIGN  AND  CONSTRUCTION 

The  ratio  y  gives  the  value  sin  d  which  defines  the  angle 

d,  as  being  the  angle  which  the  ascending  line  of  path  makes 
with  the  horizontal  line  (Fig.  94) .  We  then  have 
V  =  V  sin  e 
This  equation  shows  that  the  maximum  v  corresponds 
to  the  maximum  value  of  V  sin  d,  and  not  to  the  maximum 
value  of  sin  6;  that  is,  it  may  happen  that  by  increasing 
the  angle  d,  the  climbing  speed  will  be  decreasing  instead  of 
increasing. 


Fig.  94. 

In  Fig.  95  we  have  drawn,  for  the  already  discussed  ex- 
ample, diagrams  of  v  and  sin  d  as  functions  of  V.  We  see 
that  V  is  maximum  for  sin  6  =  0.35;  for  the  value  sin  d  = 
0.425,  which  represents  the  maximum  of  sin  6,  we  have 
V  =  29,  which  is  less  than  the  preceding  value. 

We  also  see  that  in  climbing,  the  speed  of  the  airplane  is 
less  than  that  of  ths  airplane  in  horizontal  flight,  supposing 
that  the  engine  is  run  at  full  power. 

The  maneuver  that  must  be  accomplished  by  the  pilot 
in  order  to  increase  or  decrease  the  climbing  speed,  consists 
in  the  variation  of  the  angle  of  incidence  of  the  airplane, 
by  moving  the  elevator. 

In  fact,  as  we  have  already  seen, 

W  =  10-'\AV'" 

Fixing  the  angle  of  incidence  fixes  the  value  of  X,  and 
consequently  that  of  V  necessary  for  sustentation;  the  air- 
plane then  automatically  puts  itself  in  the  climbing  line 
of  path,  to  which  velocity  V  corresponds. 

But  the  pilot  has  another  means  for  maneuvering  for 
height;  that  is,  the  variation  of  the  engine  power  by  ad- 
justing the  fuel  supply.  In  fact,  let  us  suppose  that  the 
pilot  reduces  the  power  pPi]  then  the  difference  pP2  —  Pi, 
will  decrease,  consequently  decreasing  V  and  sin  e.     If  the 


FLYING  WITH  POWER  ON 


133 


pilot  reduces  the  engine  power  to  a  point  where  pPi  —  Pi  = 
0;  the  result  will  be  z'  =  0  and  sin  0  =  0.  We  see  then  the 
possibility,  by  throttling  the  engine,  of  flying  at  a  whole 


110       120      130 
V  M.p.h. 

Fig.  95. 


140      150       160      170 


series  of  speeds,  varying  from  a  minimum  value,  which 
depends  essentially  upon  the  characteristics  of  the  airplane, 
to  a  maximum  value  which  depends  not  only  upon  the 
airplane,  but  also  upon  the  engine  and  propeller. 


CHAPTER  X 
STABILITY  AND  MANEUVERABILITY 

Let  us  consider  a  body  in  equilibrium,  either  static  or 
dynamic;  and  let  us  suppose  that  we  displace  it  a  trifle 
from  the  position  of  equihbrium  already  mentioned;  if  the 
system  of  forces  applied  to  the  body  is  such  as  to  restore 
it  to  the  original  position  of  equilibrium,  it  is  said  that  the 
body  is  in  a  state  of  stable  equilibrium. 

In  this  way  we  naturally  disregard  the  consideration  of 
forces  which  have  provoked  the  break  of  equilibrium. 
From  this  analogy,  some  have  defined  the  stability  of  the 
airplane  as  the  "tendency  to  react  on  each  break  of  equilibrium 
without  the  intervention  of  the  -pilot.''  Several  constructors 
have  attempted  to  solve  the  problem  of  stability  of  the 
airplane  by  using  solely  the  above  criterions  as  a  basis. 

In  reality  in  considering  the  stability  of  the  airplane,  the 
disturbing  forces  which  provoke  the  break  of  a  state  of 
equilibrium,  cannot  be  disregarded. 

These  forces  are  most  variable,  especially  in  rough  air, 
and  are  such  as  to  often  substantially  modify  the  resistance 
of  the  original  acting  forces.  The  knowledge  of  them  and 
of  their  laws  of  variation  is  practically  impossible;  therefore 
there  is  no  solid  basis  upon  which  to  build  a  general  theory 
of  stability. 

Nevertheless,  by  limiting  oneself  to  the  flight  in  smooth 
air,  it  is  possible  to  study  the  general  conditions  to  which 
an  airplane  must  accede  in  order  to  have  a  more  or  less 
great  intrinsic  stability. 

Let  us  consider  an  airplane  in  normal  rectilinear  hori- 
zontal flight  having  a  speed  V.  The  forces  to  which  the 
airplane  is  subjected  are: 

its  weight  TT^, 

the  propeller  thrust  T,  and 

the  total  air  reaction  R. 

134 


STABILITY  AND  MANEUVERABILITY 


135 


These  forces  are  in  equilibrium;  that  is,  they  meet  in  one 
point  and  their  resultant  is  zero  (Fig.  96). 

The  axis  of  thrust  T  generally  passes  through  the  center  of 
gravity.  Then  R  also  passes  through  the  center  of  gravity. 
Supposing  now  that  the  orientation  of  the  airplane  with 
respect  to  its  line  of  path  is  varied  abruptly,  leaving  all 
the  control  surfaces  neutral ;  the  air  reaction  R  will  change 
not  only  in  magnitude,  but 
also  in  position.  The  varia- 
tion in  magnitude  has  the 
only  effect  of  elevating  or  low- 
ering the  line  of  path  of  the 
airplane;  instead,  the  varia- 
tion in  position  introduces  a 
couple  about  the  center  of  -^ 
gravity,  which  tends  to  make 
the  airplane  turn.  If  this 
turning  has  the  effect  of  re- 
establishing the  original  posi- 
tion, the  airplane  is  stable. 
If,  however,  it  has  the  effect 
of  increasing  the  displacement, 
the  airplane  is  unstable. 

For  simplicity,  the  displacements  about  the  three  prin- 
cipal axes  of  inertia,  the  pitching  axis,  the  rolling  axis, 
and  the  directional  axis  (see  Chapter  II),  are  usually 
considered  separately. 

For  the  pitching  movement,  it  is  interesting  only  to 
know  the  different  positions  of  the  total  resultant  R  cor- 
responding to  the  various  values  of  the  angle  of  incidence. 
In  Fig.  97  a  group  of  straight  lines  corresponding  to  the  vari- 
ous positions  of  the  resultant  R  with  the  variation  of  the 
angle  of  incidence,  have  been  drawn  only  as  a  qualitative 
example.  If  we  suppose  that  the  normal  incidence  of 
flight  of  the  airplane  is  3°,  the  center  of  gravity  (because 
of  what  has  been  said  before),  must  be  found  on  the 
resultant  R^^.  Let  us  consider  the  two  positions  Gi  and 
Gi.     If  the  center  of  gravity  falls  on  Gi  the  machine  is  un- 


FiG.  96. 


136 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


stable;  in  fact  for  angles  greater  than  3°  the  resultant  is 
displaced  so  as  to  have  a  tendency  to  further  increase  the 
incidence  and  vice  versa.  If,  instead,  the  center  of  gravity- 
falls  in  G2,  the  airplane,  as  demonstrated  in  analogous 
considerations,  is  stable. 


^0" 


Fig.  97. 


In  general,  the  position  of  the  center  of  gravity  can  be 
displaced  within  very  restricted  limits,  more  so  if  we  wish 
to  let  the  axis  of  thrust  pass  near  it.  On  the  other  hand, 
it  is  not  possible  to  raise  the  wing  surfaces  much  with 
respect  to  the  center  of  gravity,  because  the  raising  would 
produce  a  partial  raising  of  the  center  of  gravity,  and 
also  because  of  constructional  restrictions. 

Then,  in  order  to  obtain  a  good  stability,  the  adoption  of 


STABILITY  AND  MANEUVERABILITY 


137 


stabilizers  is  usually  resorted  to,  which  (as  we  have  seen 
in  Chapter  II)  are  supplementary  wing  surfaces,  generally 
situated  behind  the  principal  wing  surfaces  and  making  an 
angle  of  incidence  smaller  than  that  of  the  principal  wing 
surface.  The  effect  of  stabilizers  is  to  raise  the  zone  in 
which  the  meeting  points  of  the  various  resultants  are, 
thus  facilitating  the  placing  of  the  center  of  gravity  within 
the  zone  of  stability.  Naturally  it  is  necessary  that  the 
intrinsic  stability  be  not  excessive,  in  order  that  the  man- 
euvers be  not  too  difficult  or  even  impossible. 


The  preceding  is  applied  to  cases  in  which  the  axis  of 
thrust  passes  through  the  center  of  gravity.  It  is  also  neces- 
sary to  consider  the  case,  which  may  happen  in  practice,  in 
which  the  axis  of  thrust  does  not  pass  through  the  center  of 
gravity.  Then,  in  order  to  have  equilibrium,  it  is  necessary 
that  the  moment  of  the  thrust  about  the  center  of  gravity 
T  X  ^,  be  equal  and  opposite  to  the  moment  i2  X  r  of  the 
air  reaction  (Fig.  98).  Let  us  see  which  are  the  conditions 
for  stability. 

To  examine  this,  it  is  necessary  to  consider  the  meta- 
centric curve,  that  is,  the  enveloping  curve  of  all  the  resultants 
(Fig.  99).  Starting  from  a  point  0,  let  us  take  a  group 
of  segments  parallel  and  equal  to  the  various  resultants  Ri 


138 


AIRPLANE  DESIGN  AND  CONSTRUCriON 


corresponding  to  the  normal  value  of  the  speed.  Let  us 
consider  one  of  the  resultants,  for  instance  Ri.  At  point 
A,  where  Ri  is  tangent  to  the  metacentric  curve  a,  let  us 
draw  oa  parallel  to  h,  which  is  tangent  to  curve  /3  at  5  the 
extreme  end  of  R^. 

We  wish  to  demonstrate  that  the  straight  line  oa  is  a  locus 
of  points  such  that  if  the  center  of  gravity  falls  on  it,  and  the 
equilibrium  exists  for  a  value  of  the  angle  of  incidence,  this 
equilibrium  will  exist  for  all  the  other  values  of  incidence 


Fig.  99. 

(understanding  the  speed  to  be  constant).  In  other  words, 
we  wish  to  demonstrate  that  oa  is  a  locus  of  the  points  corre- 
sponding to  the  indifferent  equilibrium,  and  consequently  it 
divides  the  stability  zone  from  the  instability  zone. 

Let  us  suppose  that  the  center  of  gravity  falls  at  G  on  oa, 
and  that  the  incidence  varies  from  the  value  i  (for  which  we 
have  the  equilibrium)  to  a  value  infinitely  near  i'.  If  we 
demonstrate  that  the  moment  of  R'i  about  G  is  equal  to  the 
moment  of  Ri,  the  equilibrium  will  be  demonstrated  to  be 
indifferent.  Starting  from  C  point  of  the  intersection  of 
Ri  and  R'i,  let  us  take  two  segments  CD  and  CD'  equal  to 
the  value  Ri  and  R'i  respectively.  The  joining  line  DD' 
is  parallel  to  BB' ;  now  when  i'  differs  infinitely  little  from 
i,  BE'  becomes  tangent  to  the  curve  /8  at  point  B;  conse- 
quently, DD'  becomes  parallel  to  tangent  6;  that  is,  also 
to  straight  line  ao.     Now  point  C,  if  i'  differs  infinitely 


STABILITY  AND  MANEUVERABILITY  139 

little  from  i,  is  coincident  with  A  (and  consequently  the 
segments  GC  with  GA)  then  the  two  triangles  GCD'  and 
GCD  (which  measure  the  moment  of  Ri  and  R'i  with 
respect  to  G),  become  equal,  as  they  have  common  bases 
and  have  vertices  situated  on  a  line  parallel  to  the  bases: 
that  is,  the  equihbrium  is  indifferent. 

To  find  which  are  the  zones  of  stabilitj^  and  instability, 
it  suffices  to  suppose  for  a  moment  that  the  center  of 
gravity  falls  on  the  intersection  of  the  propeller  axis  and 
the  resultant  Ri,  then  the  center  of  gravity  will  be  on  Ri', 
and  since  A  is  on  the  line  oa,  it  will  be  a  point  of  indifferent 
equilibrium,  consequently  dividing  the  line  Ri  into  two  half 
lines  corresponding  to  the  zones  of  stability  and  instability. 
From  what  has  already  been  said,  it  will  be  easy  to  establish 
the  half  line  which  corresponds  to  the  stability,  and  thus 
the  entire  zone  of  stability  will  be  defined. 

The  calculation  of  the  magnitude  of  the  moments  of 
stabiUty,  is  not  so  difficult  when  the  metacentric  curve 
and  the  values  i?i  for  a  given  speed  are  known. 

The  foregoing  was  based  upon  the  supposition  that  the 
machine  would  maintain  its  speed  constant,  even  though 
varying  its  orientation  with  respect  to  the  line  of  path. 
Practically,  it  happens  that  the  speed  varies  to  a  certain 
extent;  then  a  new  unknown  factor  is  introduced,  which 
can  alter  the  values  of  the  restoring  couple.  Nevertheless, 
it  should  be  noted  that  these  variations  of  speed  are  never 
instantaneous. 

In  referring  to  the  elevator,  in  Chapter  II,  we  have  seen 
that  its  function  is  to  produce  some  positive  and  negative 
couples  capable  of  opposing  the  stabilizing  couples,  and 
consequently  permitting  the  machine  to  fly  with  different 
values  of  the  angle  of  incidence.  All  other  conditions  being 
the  same  (moment  of  inertia  of  the  machine,  braking 
moments,  etc.),  the  mobility  of  a  machine  in  the  longitudi- 
nal sense,  depends  upon  the  ratio  between  the  value  of  the 
stabilizing  moments  and  that  of  the  moments  it  is  possible 
to  produce  by  maneuvering  the  elevator.  A  machine  with 
great  stability  is  not  very  maneuverable.    On  the  other  hand, 


140  AIRPLANE  DESIGN  AND  CONSTRUCTION 

a  machine  of  great  maneuverability  can  become  dangerous, 
as  it  requires  the  continuous  attention  of  the  pilot. 

An  ideal  machine  should,  at  the  pilot's  will,  be  able  to 
change  the  relative  values  of  its  stability  and  maneuvera- 
bility ;  this  should  be  easy  by  adopting  a  device  to  vary  the 
ratios  of  the  controlling  levers  of  the  elevator.  In  this  way, 
the  other  advantage  would  also  be  obtained  of  being  able 
to  decrease  or  increase  the  sensibility  of  the  controls  as  the 
speed  increases  or  decreases.  Furthermore,  we  could 
resort  to  having  strong  stabilizing  couples  prevail  normally 
in  the  machine,  it  being  possible  at  the  same  time  to  imme- 
diately obtain  great  maneuverability  in  cases  where  it 
became  necessary. 

As  to  lateral  stability,  it  can  be  defined  as  the  tendency  of 
the  machine  to  deviate  so  that  the  resultant  of  the  forces 
of  mass  (weight,  and  forces  of  inertia)  comes  into  the  plane  of 
symmetry  of  the  airplane. 

When,  for  any  accidental  cause  whatever,  an  airplane 
inclines  itself  laterally,  the  various  applied  forces  are  no 
longer  in  equilibrium,  but  have  a  resultant,  which  is  not 
contained  in  the  plane  of  symmetry. 

Then  the  line  of  path  is  no  longer  contained  in  the  plane 
of  symmetry  and  the  airplane  drifts.  On  account  of  this 
fact,  the  total  air  reaction  on  the  airplane  is  no  longer 
contained  in  the  plane  of  symmetry,  but  there  is  a  drift 
component,  the  line  of  action  of  which  can  pass  through, 
above  or  below  the  center  of  gravity. 

In  the  first  case,  the  moment  due  to  the  drift  force  about 
the  center  of  gravity  is  zero,  consequently,  if  the  pilot  does 
not  intervene  by  maneuvering  the  ailerons,  the  machine 
will  gradually  place  itself  in  the  course  of  drift,  in  which  it 
will  maintain  itself.  In  the  other  two  cases,  the  drift  com- 
ponent will  have  a  moment  difTerent  from  zero,  and  which 
will  be  stabilizing  if  the  axis  of  the  drift  force  passes  above 
the  center  of  gravity;  it  will  instead,  be  an  overturning 
moment  if  this  axis  passes  below  the  center  of  gravity.  To 
obtain  a  good  lateral  stability,  it  is  necessary  that  the  axis 
of  the  drift  component  meet  the  plane  of  symmetry  of 


STABILITY  AND  MANEUVERABILITY 


141 


the  machine  at  a  point  above  the  horizontal  Une  contained 
in  the  plane  of  symmetry  and  passing  through  the  center  of 
gravity;  that  point  is  called  the  center  of  drift;  thus  to 
obtain  a  good  transversal  stability  it  is  necessary  that  the  center 
of  drift  fall  above  the  horizontal  line  drawn  through  the  center 
of  gravity  (Fig.  100).  This  result  can  be  obtained  by 
lowering  the  center  of  gravity,  or  by  adopting  a  vertical 
fin  situated  above  the  center  of  gravity,  or,  as  it  is  generally 
done,  by  giving  the  wings  a  transversal  inclination  usually 
called  ''dihedral".  Naturally  what  has  been  said  of  longi- 
tudinal stability,  regarding  the  convenience  of  not  having 

IfCenhr  of  Drift  falls  on  fhislone.  the  Machine  is  Lahratly  Stable. 


If  Cen-kr  of  Drift  falls  on  this  Zone  the  Machine  is  Laterally  Unskibte 
Fig.   100. 


it  excessive,  so  as  not  to  decrease  the  maneuverability  too 
much,  can  be  applied  to  lateral  stability. 

Let  us  finally  consider  the  problems  pertaining  to 
directional  stability.  The  condition  necessary  for  an 
airplane  to  have  good  stability  of  direction  is,  by  a  series  of 
considerations  analogous  to  the  preceding  one,  that  the  center 
of  drift  fall  behind  the  vertical  line  drawn  through  the 
center  of  gravity  (Fig.  101).  This  is  obtained  by  adopting 
a  rear  fins. 

By  adding  Figs.  100  and  101,  we  have  Fig.  102  which  shows 
that  the  center  of  drift  must  fall  in  the  upper  right 
quadrant. 

Summarizing,  we  may  say  that  it  is  possible  to  build 
machines  which,  in  calm  air,  are  provided  with  a  great  in- 
trinsic stability;  that  is,  having  a  tendency  to  react  every 
time  the  line  of  path  tends  to  change  its  orientation  rela- 
tively to  the  machine.     It  is  necessary,  however,  that  this 


142 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


tendency  be  not  excessive,  in  order  not  to  decrease  the 
maneuverability  which  becomes  an  essential  quality 
in  rough  air,  or  when  acrobatics  are  being  accomplished. 


If  Center  of  Dri-ff  falls  on  ihis 
Zone  fhe  Machine  has  ._ 
Directional 
Instabilitij. 


If  Center  of  Drift  fa  lis  on  this  Zone 
the  Machine  has  Directional  StabilitLj. 


Fig.  101. 


Thus  far  we  have  considered  the  flight  with  the  engine 
running.  Let  us  now  suppose  that  the  engine  is  shut  off. 
Then  the  propeller  thrust  becomes  equal  to  zero.     Let  us 


Zone  within  nhich  the  Center  pf  Drift  must 
'/  in  Order  that  the  Machine  be  Trans  versa II tj 
and  Directionallu  Siable 


Fig.   102. 


first  consider  the  case  in  which  the  axis  of  thrust  passes 
through  the  center  of  gravity. 

In  this  case,  the  disappearance  of  the  thrust  will 
not  bring  any  immediate  disturbance  in  the  longitudinal 
equilibrium  of  the  airplane.     But  the  equihbrium  between 


STABILITY  AND  MANEUVERABILITY 


143 


144  AIRPLANE  DESIGN  AND  CONSTRUCTION 

weight,  thrust,  and  air  reaction,  will  be  broken,  and  the 
component  of  head  resistance,  being  no  longer  balanced  by 
the  propeller  thrust,  will  act  as  a  brake,  thereby  reducing 
the  speed  of  the  airplane ;  as  a  consequence,  the  reduction  of 
speed  brings  a  decrease  in  the  sustaining  force;  thus  equi- 
librium between  the  component  of  sustentation  of  the  air 
reaction  and  the  weight  is  broken,  and  the  line  of  path 
becomes  descendent;  that  is,  an  increase  of  the  angle  of 
incidence  is  caused;  a  stabilizing  couple  is  then  produced, 
tending  to  restore  the  angle  of  incidence  to  its  normal 
value;  that  is,  tending  to  adjust  the  machine  for  the 
descent. 

The  normal  speed  of  the  airplane  then  tends  to  restore 
itself;  the  inclination  of  the  line  of  path  and  the  speed  will 
increase  until  they  reach  such  values  that  the  air  reaction 
becomes  equal  and  of  opposite  direction  to  the  weight  of 
the  airplane  (Fig.  103).  Practically,  it  will  happen  that 
this  position  (due  to  the  fact  that  the  impulse  impressed 
on  the  airplane  by  the  stabilizing  couple  makes  it  go  beyond 
the  new  position  of  equilibrium)  is  not  reached  until  after 
a  certain  number  of  oscillations.  Let  us  note  that  the  glid- 
ing speed  in  this  case  is  smaller  than  the  speed  in  normal 
flight;  in  fact  in  normal  flight,  the  air  reaction  must  balance 
W  and  T,  and  is  consequently  equal  to  y/ W^  +  T^; 
in  gliding  instead,  it  is  equal  to  W;  that  is,  calling  R'  and 
R"  respectively,  the  air  reaction  in  normal  flight  and  in 
gliding  flight, 

R^  ^  yw  +  T^  ^  ITVTl 

R"  W  V    "^  W^ 

and  calling  V  and  V"  the  respective  speeds,  we  will  have 

-=  K-  W 

r.,        V^"       \^ 


^'    '«'    ux; 


Y"       \R"      \"^IF' 

When  the  axis  of  thrust  does  not  pass  through  the  center 
of  gravity,  as  the  engine  is  shut  off,  a  moment  is  produced 
equal  and  of  opposite  direction  to  the  moment  of  the  thrust 
with  respect  to  the  center  of  gravity.     Thus  if  the  axis 


STABILITY  AND  MANEUVERABILITY  145 

of  thrust  passes  above  the  center  of  gravity,  the  moment 
developed  will  tend  to  make  the  airplane  nose  up.  If 
instead,  it  passes  below  the  center  of  gravity,  the  moment 
developed  will  tend  to  make  the  airplane  nose  down. 
If  the  airplane  is  provided  with  intrinsic  stability,  a  gliding 
course  will  be  established,  with  an  angle  of  incidence 
different  from  that  in  normal  flight,  and  which  will  be 
greater  in  case  the  axis  of  thrust  passes  above  the  center 
of  gravity,  and  smaller  in  the  opposite  case.  The  speed  of 
gliding  in  the  first  case,  will  be  smaller,  and  greater  in  the 
second  case  than  the  speed  obtainable  when  the  axis  of 
thrust  passes  through  the  center  of  gravity. 

Naturally,  the  pilot  intervening  by  maneuvering  the 
control  surfaces  can  provoke  a  complete  series  of  equilibrium, 
and  thus,  of  paths  of  descent. 

We  have  seen  that  when  a  stabilizing  couple  is  intro- 
duced, the  airplane  does  not  immediately  regain  its  original 
equilibrium,  but  attains  it  by  going  through  a  certain 
number  of  oscillations  of  which  the  magnitude  is  directly 
proportional  to  the  stabilizing  couple;  in  calm  air,  the  oscilla- 
tions diminish  by  degrees,  more  or  less  rapidly  according  to 
the  importance  of  the  dampening  couples  of  the  machine. 

In  rough  air,  instead,  sudden  gusts  of  wind  may  be  en- 
countered which  tend  to  increase  the  amplitude  of  the 
oscillations,  thus  putting  the  machine  in  a  position  to  pro- 
voke a  definite  brake  of  the  equilibrium,  and  consequently 
to  fall.  That  is  why  the  pilot  must  have  complete  con- 
trol of  the  machine;  that  is,  machines  must  be  provided 
with  great  maneuverability  in  order  that  it  may  be  possible, 
at  the  pilot's  will,  to  counteract  the  disturbing  couple,  as 
well  as  to  dampen  the  oscillations.  In  other  words,  if  the 
controls  are  energetic  enough,  the  maneuvers  accompUshed 
by  the  pilot  can  counteract  the  periodic  movements,  thereby 
greatly  decreasing  the  pitching  and  rolling  movements. 

In  order  to  accomplish  acrobatic  maneuvers  such  as 
turning  on  the  wing,  looping,  spinning,  etc.,  it  is  neces- 
sary to  dispose  of  the  very  energetic  controls,  not  so  much 
to  start  the  maneuvers  themselves,  as  to  rapidly  regain  the 


146  AIRPLANE  DESIGN  AND  CONSTRUCTION 

normal  position  of  equilibrium  if  for  any  reason  whatever 
the  necessity  arises. 

Let  us  consider  an  airplane  provided  with  intrinsic  auto- 
matic stability,  as  being  left  in  the  air  with  a  dead  engine 
and  insufficient  speed  for  its  sustentation.  The  airplane 
will  be  subjected  to  two  forces,  weight  and  air  reaction, 
which  do  not  balance  each  other,  as  the  air  reaction  can 
have  any  direction  whatever  according  to  the  orientation 
of  the  airplane  and  the  relative  direction  of  the  line  of 
path. 

Let  us  consider  two  components  of  the  air  reaction,  the 
vertical  component  and  the  horizontal  component.  The 
vertical  component  partly  balances  the  weight;  the  differ- 
ence between  the  weight  and  this  component  measures 
the  forces  of  vertical  acceleration  to  which  the  airplane  is 
subjected.  The  horizontal  component,  instead,  can  only 
be  ba^.anced  by  a  horizontal  component  of  acceleration;  in 
other  words,  it  acts  as  a  centripetal  force,  and  tends  to 
make  the  airplane  follow  a  circular  line  of  path  of  such 
radius  that  the  centrifugal  force  which  is  thereby  de- 
veloped, may  establish  the  equilibrium.  Thus,  an  air- 
plane left  to  itself,  falls  in  a  spiral  line  of  path,  which  is 
called  spinning.  Let  us  suppose,  now,  that  the  pilot  does 
not  maneuver  the  controls;  then,  if  the  machine  is  pro- 
vided with  intrinsic  stability,  it  will  tend  to  orient  itself 
in  such  a  way  as  to  have  the  line  of  path  situated  in  its  plane 
of  symmetry  and  making  an  angle  of  incidence  with  the 
wing  surface  equal  to  the  angle  for  which  the  longitudinal 
equilibrium  is  obtained.  That  is,  the  machine  will  tend 
to  leave  the  spiral  fall,  and  put  itself  in  the  normal 
gliding  line  of  path.  Naturally  in  order  that  this  may 
happen,  a  certain  time,  and,  w^hat  is  more  important,  a 
certain  vertical  space,  are  necessary.  The  disposable  ver- 
tical space  may  happen  to  be  insufficient  to  enable  the 
machine  to  come  out  of  its  course  in  falling;  in  that  case  a 
crash  will  result. 

We  see  then  what  a  great  convenience  the  pilot  has  in 
being  able  to  dispose  of  the  energetic  controls  which  can 


STABILITY  AND  MANEUVERABILITY  147 

be    properly    used   to   decrease   the   space    necessary    for 
restoring  the  normal  equilibrium. 

Summarizing,  we  can  mention  the  following  general 
criterions  regarding  the  intrinsic  stability  of  a  machine : 

1.  It  is  necessary  that  the  airplane  be  provided  with  in- 
trinsic stability  in  calm  air,  in  order  that  it  react  auto- 
matically to  small  normal  breaks  in  equilibrium,  without 
requiring  an  excessive  nervous  strain  from  the  pilot; 

2.  This  stability  must  not  be  excessive  in  order  that  the 
maneuvers  be  not  too  slow  or  impossible;  and 

3.  It  is  necessary  that  the  maneuvering  devices  be  such 
as  to  give  the  pilot  control  of  the  machine  at  all  times. 

Before  concluding  the  "chapter  it  may  not  be  amiss  to 
say  a  few  words  about  mechanical  stabilizers.  Their  scope 
is  to  take  the  place  of  the  pilot  by  operating  the  ordi- 
nary maneuvering  devices  through  the  medium  of  proper 
servo-motors.  Naturally,  apparatuses  of  this  kind,  cannot 
replace  the  pilot  in  all  maneuvers;  it  is  sufficient  only  to 
mention  the  landing  maneuver  to  be  convinced  of  the 
enormous  difficulty  offered  by  a  mechanical  apparatus 
intended  to  guide  such  a  maneuver.  Essentially,  their  use 
should  be  limited  to  that  of  replacing  the  pilot  in  normal 
flight,  thereby  decreasing  his  nervous  fatigue,  especially 
during  adverse  atmospheric  conditions. 

We  can  then  say  at  once  that  a  mechanical  stabilizer  is 
but  an  apparatus  sensible  to  the  changes  in  equilibrium 
which  is  desired  to  be  avoided,  or  sensible  to  the  causes 
which  produce  them,  and  capable  of  operating,  as  a  conse- 
quence of  its  sensibility,  a  servo-motor,  which  in  turn 
maneuvers  the  controls.  We  can  group  the  various  types 
of  mechanical  stabilizers,  up  to  date,  into  three  categories: 

1.  Anemometric, 

2.  Clinometric,  and 

3.  Inertia  stabilizer. 

There  are  also  apparatus  of  compound  type,  but  their 
parts  can  always  be  referred  to  one  of  the  three  preceding 
categories. 


148 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


1.  The  anemometric  stabilizers  are,  principally,  speed 
stabilizers.  They  are,  in  fact,  sensible  to  the  variations  of 
the  relative  speed  of  the  airplane  with  respect  to  the  air, 
and  consequently  tend  to  keep  that  speed  constant. 

Schematically  an  anemometric  stabilizer  consists  of  a 
small  surface  A  (Fig.  104),  which  can  go  forward  or  back- 
ward under  the  action  of  the  air  thrust  R,  and  under  the 
reaction  of  a  spring  S.  The  air  thrust  R,  is  proportional  to 
the  square  of  the  speed.  When  the  relative  speed  is  equal 
to  the  normal  one,  a  certain  position  of  equilibrium  is  ob- 
tained; if  the  speed  increases,  R  increases  and  the  small 
disk  goes  backward  so  as  to  further  compress  the  spring. 
If,  instead,  the  speed  decreases,  R  will  decrease,  and  the 


Fig.  104. 


small  disk  will  go  forward  under  the  spring  reaction. 
Through  rod  S,  these  movements  control  a  proper  servo- 
motor which  maneuvers  the  elevator  so  as  to  put  the  air- 
plane into  a  climbing  path  when  the  speed  increases,  and 
into  a  descending  path  when  the  speed  decreases. 

Such  functioning  is  logical  when  the  increase  or  decrease 
of  the  relative  speed  depends  upon  the  airplane,  for  instance, 
because  of  an  increase  or  decrease  of  the  motive  power. 
The  maneuver  however,  is  no  longer  logical  if  the  increase 
of  relative  speed  depends  upon  an  impetuous  gust  of  wind 
which  strikes  the  airplane  from  the  bow;  in  fact,  this  man- 
euver would  aggravate  the  effect  of  the  gust,  as  it  would 
cause  the  airplane  to  offer  it  a  greater  hold. 


STABILITY  AND  MANEUVERABILITY  149 

Thus  we  see  that  an  anemometric  stabilizer,  used  by 
itself,  can  give,  as  it  is  usually  said,  counter-indications, 
which  lead  to  false  maneuvers. 

In  consideration  of  this,  the  Doutre  stabilizer,  which  is 
until  now,  one  of  the  most  successful  of  its  kind  ever  built, 
is  provided  with  certain  small  masses  sensible  to  the  inertia 
forces,  and  of  which  the  scope  is  to  block  the  small  anemo- 
metric blade  when  the  increase  of  relative  speed  is  due  to 
a  gust  of  wind. 

2.  Several  types  of  clinometric  stabilizers  have  been  pro- 
posed; the  mercury  level,  the  pendulum,  the  gyroscope,  etc. 

The  common  fault  of  these  stabilizers  is  that  they  are 
sensible  to  the  forces  of  inertia. 

The  best  clinometric  stabilizer  that  has  been  built,  and 
which  is  to-day  considered  the  best  in  existence,  is  the 
Sperry  stabilizer. 

It  consists  of  four  gyroscopes,  coupled  so  as  to  insure  the 
perfect  conservation  of  a  horizontal  plane,  and  to  eliminate 
the  effect  of  forces  of  inertia,  including  the  centrifugal 
force. 

The  relative  movements  of  the  airplane  with  respect  to 
the  gyroscope  system,  control  the  servo-motor,  which  in 
turn  actions  the  elevator  and  the  horizontal  stabilizing 
surfaces.  A  special  lever,  inserted  between  the  servo- 
motor and  the  gyroscope,  enables  the  pilot  to  fix  his  machine 
for  climbing  or  descending;  then  the  gyroscope  insures  the 
wanted  inclination  of  the  line  of  path. 

There  is  a  small  anemometric  blade  which  fixes  the  air- 
plane for  the  descent  when  the  relative  speed  decreases. 
A  special  pedal  enables  the  detachment  of  the  stabilizer 
and  the  control  of  the  airplane  in  a  normal  way. 

3.  The  inertia  stabilizers  are,  in  general,  made  of  small 
masses  which  are  utilized  for  the  control  of  servo-motors; 
and  which,  under  the  action  of  the  inertia  forces  and 
reacting  springs,  undergo  relative  displacement. 

In  general,  the  disturbing  cause,  whatever  it  may  be,  can 
be  reduced,  with  respect  to  the  effects  produced  by  it,  to  a 
force  applied  at  the  center  of  gravity,  and  to  a  couple. 


150  AIRPLANE  DESIGN  AND  CONSTRUCTION 

The  force  admits  three  components  parallel  to  three  prin- 
cipa  axes,  and  consequently  originates  three  accelerations 
(longitudinal,  transversal,  and  vertical).  The  couple  can 
be  resolved  into  three  component  couples,  which  originate 
three  angular  accelerations,  having  as  axis  the  same  principal 
axis  of  inertia.  A  complete  inertia  stabilizer  should  be 
provided  with  three  linear  accelerometers  and  three  angular 
accelerometers,  which  would  measure  the  six  aforesaid 
components. 


CHAPTER  XI 
FLYING  IN  THE  WIND 

Let  us  first  of  all  consider  the  case  of  a  wind  which  is 
constant  in  du-ection  as  well  as  in  speed. 

Such  wind  has  no  influence  upon  the  stabihty  of  the  air- 
plane, but  influences  solely  its  speed  relative  to  the  ground. 

Let  V  be  the  speed  proper  of  the  airplane,  and  W  the 
speed  of  the  wind;  in  flight  the  airplane  can  be  considered 
as  a  body  suspended  in  a  current  of  water,  of  which  the 


/^ 

/ 

■  \ 

1 

1 

._u^_ 

b 

i 

/I 

/  1 

^^ 

.--'' 

Fig. 

105. 

speed  U,  with  respect  to  the  ground,  becomes  equal  to  the 
resultant  of  the  two  speeds  V  and  W  (Fig.  105). 

We  see  then,  that  the  existence  of  a  wind  W  changes 
speed  V  not  only  in  dimension  but  also  in  direction. 

Furthermore,  if  from  a  point  A  we  wish  to  reach  another 
point  B,  and  co  is  the  angle  which  the  wind  direction  makes 
with  the  Une  of  path  AB,  it  is  necessary  to  make  the  air- 
plane fly  not  in  direction  AB,  but  in  a  direction  AO  making 
an  angle  8  with  AB  such  that  the  resulting  speed  U  is  in 

151 


152  AIRPLANE  DESIGN  AND  CONSTRUCTION 

the  direction  AB.     By  a  known  geometrical  theorem,  we 
have 


U  =  VF2  -\-W'  -  2UW  cos  (180°  -  5  -  a,) 

and 

•     .       "^^    • 
sm  5  =  ^  sm  w 

A  simple  diagram  is  given  in  Fig.  106,  which  enables  the 
calculation  of  angle  5,  when  the  speeds  V  and  W,  and  the 
angle  to  which  the  wind  makes  with  the  line  of  flight  to  be 
covered,  is  known. 

This  diagram  is  constituted  of  concentric  circles,  whose 
radius  represents  the  speed  of  the  wind,  and  of  a  series  of 
radii,  of  which  the  angles  with  respect  to  the  line  OA  give 
the  angles  to  between  the  line  of  path  and  the  wind.  Let 
us  find  the  angle  5  of  drift,  at  which  the  airplane  must  fly, 
for  example,  with  a  30  m.p.h.  wind  making  90°  with  the 
line  of  path  (the  drift  angle  of  the  trajectory  must  not  be 
confused  with  the  angle  of  drift  of  the  airplane  with  respect 
to  the  trajectory,  of  which  we  have  discussed  in  the  chap- 
ter on  stability).  Let  us  take  point  B  the  intersection 
of  the  circle  of  radius  30  with  the  line  BO  which  makes 
90°  with  OA ;  making  B  the  center,  and  speed  V  of  the  air- 
plane the  radius,  which  we  shall  suppose  equal  to  100  m.p.h., 
we  shall  have  point  C  which  determines  U  and  8 ;  in  fact  OC 
equals  U,  and  angle  BCO  equals  6.  In  our  case  U  = 
95.5  m.p.h.,  and  sin  8  =  0.3. 

The  speed  of  the  wind  varies  within  wide  limits,  and  can 
rise  to  110  miles  per  hour,  or  more;  naturally  it  then  be- 
comes a  violent  storm. 

A  wind  of  from  7  to  8  miles  an  hour  is  scarcely  percepti- 
ble by  a  person  standing  still.  A  wind  of  from  13  to  14 
miles,  moves  the  leaves  on  the  trees;  at  20  miles  it  moves 
the  small  branches  on  the  trees  and  is  strong  enough  to 
cause  a  flag  to  wave.  At  35  miles  the  wind  already  gathers 
strength  and  moves  the  large  branches;  at  80  miles,  light 
obstacles  such  as  tiles,  slate,  etc.,  are  carried  away;  the  big 
storms,  as  we  have  already  mentioned,  even  reach  a  speed  of 


FLYING  IN  THE  WIND 


153 


110  miles  an  hour.  As  airplanes  have  actually  reached 
speeds  greater  than  110  m.p.h.  (even  160  m.p.h.),  it  would 
be  possible  to  fly  and  even  choose  direction  from  point  to 
point  in  violent  wind  storms.     But  the  landing  maneuver, 


consequently,  becomes  very  dangerous.  At  least  during 
the  present  stage  of  constructive  technique,  it  is  wise  not 
to  fly  in  a  wind  exceeding  50  to  60  m.p.h.  After  all,  such 
winds  are  the  highest  that  are  normally  had,  the  stronger 
ones  being  exceptional  and  localized.     On  the  contrary, 


154 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


for  the  aims  of  an  organization,  for  instance,  for  aerial  mail 
service,  it  would  be  useless  to  take  winds  higher  than  30 
to  40  m.p.h.  into  consideration. 

If  we  call  M  the  distance  to  be  covered  in  miles,  V  the 
speed  of  the  airplane  in  m.p.h.,  and  W  the  maximum  speed 
in  m.p.h.  of  the  wind  to  be  expected,  the  travelling  time  in 
hours,  when  the  wind  is  contrary,  will  be 


L  = 


M 


M 


V  -W 


X 


-^ 


200 


50  100  150  200 

V    M.p.h 

Fig.    107. 


When  the  wind  is  zero  the  travelling  time  will  be 

M 


consequently 


L  =  loX 


V 


1  - 


w 


FLYING  IX  THE  WIND 


155 


Supposing  that  we  admit,  for  instance  in  mail  service, 
a  maximum  wind  of  35  m.p.h.,  a  diagram  can  easily  be 
drawn  which  for  every  value  of  speed  V,  will  give  the  value 

100   ^  which  measures  the  percent  increase  in  the  travel- 
to 

ling  time  (Fig.  107). 

This  diagram  shows  that  the  travelling  time  tends  to 
become  infinite  when  V  approaches  the  value  of  35  m.p.h. 

L 
To 


For  each  value  of  V  lower  than  35  m.p.h.  the  value  100 


is    negative;    that  is,   the  airplane  having  such  a  speed, 
and  flying  against  a  wind  of  35  m.p.h.  would,  of  course, 


retrocede.  As  V  increases  above  the  value  35,  the  term 
100    f    decreases;    for    V  =  100    we    have    for    instance 

100    f  =  154   per    cent.;  for  V  =130,     100  "   =   137    per 

to  ''o 

cent.,  etc.  We  see  then,  because  of  contrary  wind,  that 
the  per  cent  increase  in  the  travelling  time,  is  inversely 
proportional  to  the  speed. 

Before  beginning  a  discussion  on  the  effect  of  the  wind 
upon  the  stability  of  the  airplane,  it  is  well  to  guard  against 
an  error  which  may  be  made  w^hen  the  speed  of  an  airplane 
is  measured  by  the  method  of  crossing  back  and  forth 
between  two  parallel  sights.  Let  AA'  and  BB'  be  the  two 
parallel  sights  (Fig.  108).  Let  us  suppose  that  a  wind  of 
speed  W  is  blowing  parallel  to  the  line  joining  the  parallel 
sights.  Let  ti  be  the  time  spent  by  the  airplane  in  covering 
the  distance  D  in  the  direction  of  A  A'  to  BB',  and  ^2  the 


156  AIRPLANE  DESIGN  AND  CONSTRUCTION 

time  spent  to  cover  the  distance  in  the  opposite  direction. 
It  would  be  an  error  to  calculate  the  speed  of  the  airplane 
by  dividing  the  space  2D  by  the  sum  ti  +  U.  In  fact  the 
speed  in  going  from  A  A'  to  BB'  is  equal  to 

D 


''    u 


and  in  going  the  other  way 


V  -W  =  ^ 

By  adding  the  two  above  equations :  member  to  member,  we 
have 

27  =  5  +  ^ 

U  to 


that  is 


J.      ,JD   ,    D\ 


Now  this  expression  has  a  value  absolutely  different  from 

2D 

the  other  - — r—r-     For  example :  supposing  D  =  2  miles,  ti 

tl   -f-  02 

=  0.015  hours,  and  ^2  =  0.023  hours,  we  will  have 


while 

2D  4 


h  +  U       0.015  +  0.023 


105  m.p.h. 


When  the  speed  of  the  wind  is  constant  in  magnitude 
and  direction,  the  airplane  in  flight  does  not  resent  any 
effect  as  to  its  stability.  But  the  case  of  uniform  wind 
is  rare,  especially  when  its  speed  is  high.  The  ampli- 
tude of  the  variation  of  normal  winds  can  be  considered 
proportionally  to  their  average  speed.  Some  observations 
made  in  England  have  given  either  above  or  below  23  per 
cent,  as  the  average  oscillations;  and  either  more  or  less 
than  33  per  cent,  as  the  maximum  oscillation.  In  certain 
cases,  however,  there  can  be  brusque  or  sudden  variations 
of  even  greater  amplitude. 


FLYING  IN  THE  WIND  157 

Furthermore,  the  wind  can  vary  from  instant  to  instant 
also  in  direction,  especially  when  close  to  broken  ground. 
In  fact,  near  broken  ground,  the  agitated  atmosphere  pro- 
duces the  same  phenomena  of  waves,  suctions,  and  vortices, 
which  are  produced  when  sea  waves  break  on  the  rocks. 

If  the  airplane  should  have  a  mass  equal  to  zero,  it 
would  instantaneously  follow  the  speed  variations  of 
the  air  in  which  it  is  located;  that  is,  there  would  be  a 
complete  dragging  effect.  As  airplanes  have  a  con- 
siderable mass  they  consequently  follow  the  disturbance 
only  partially. 

It  is  then  necessary  to  consider  beside  the  partial  dragging 
effect,  also  the  relative  action  of  the  wind  on  the  airplane, 
action  which  depends  upon  the  temporary  variation  of  the 
relative  speed  in  magnitude  as  well  as  in  direction.  The 
reaction  of  the  air  upon  the  airplane  takes  a  different  value 
than  the  normal  reaction,  and  the  effect  is  that  at  the  center 
of  gravity  of  the  airplane  a  force  and  a  couple  (and  conse- 
quently a  movement  of  translation  and  of  rotation),  are 
produced. 

We  have  seen  that  in  normal  flight  the  sustaining  com- 
ponent L  of  the  air  reaction,  balances  the  weight.  That  is, 
we  have 

L  =  m-'\AV^ 

If  the  relative  speed  V  varies  in  magnitude  and  direction, 
the  second  term  of  the  preceding  equation  will  become 
10~^X^A  V^,  and  in  general  we  will  have 

lO-^V  X  Ax  V"'  J  10-'\AV- 

Consequently  we  shall  have  first  of  all,  an  excess  or  deficiency 
in  sustentation  and  then  the  airplane  will  take  either  a 
climbing  or  descending  curvilinear  path,  and  will  undergo 
such  an  acceleration  that  the  corresponding  forces  of  inertia 
will  balance  the  variation  of  sustentation. 


158  AIRPLANE  DESIGN  AND  CONSTKL'CTWN 

If,  for  instance,  the  sustentation  suddenly  decreases,  the 
Une  of  path  will  bend  downward.  In  such  a  case,  all  the 
masses  composing  the  airplane,  including  the  pilot,  will 
undergo  an  acceleration  g'  contrary  to  the  acceleration  due 
to  gravity  g. 

If  m  is  the  mass  of  the  pilot,  his  apparent  weight  will  no 
longer  be  mg  but  m(g  —  g') ;  if  it  were  that  g'>g,  the  relative 
weight  of  the  pilot  with  respect  to  the  airplane  would 
become  negative,  and  tend  to  throw  the  pilot  out  of  the 
airplane.  Thence  comes  the  necessity  of  pilots  and 
passengers  strapping  themselves  to  their  seats. 

Let  us  suppose  that  an  airplane  having  a  speed  F  undergoes 
a  frontal  shock  of  a  gust  increasing  in  intensity  from  W  to 
W  +  aT^;  if  the  mass  of  the  airplane  is  big  enough,  the 
relative  speed  (at  least  at  the  first  instant),  will  pass  from 
the  value  V  to  that  of  V  +  ATF;  the  value  of  the  air  reaction 
which  was  proportional  to  V^  will  become  proportional  to 
{V  +  AT7)2;  the  percentual  variation  of  reaction  on  the  wing 
surface  will  then  be 

(F  +  AWy-  -  V  _  2  X  V  X  A  W  +  (aW) 

72  ~  Y2 


=  2f  Wf 


that  is,  it  will  be  inversely  proportional  to  the  speed  of  the 
airplane.  Great  speeds  consequently  are  convenient  not 
only  for  reducing  the  influence  of  the  wind  on  the  length 
of  time  for  a  given  space  to  be  covered,  but  also  in  order  to 
become  more  independent  of  the  influence  of  the  wind  gusts. 
Let  us  now  consider  a  variation  in  the  direction  of  the 
wind.  Let  us  first  suppose  that  this  variation  modifies 
only  the  angle  of  incidence  i;  then  the  value  X  will  change. 
For  a  given  variation  Ai  of  i,  the  percent  variation  of  X 
will  be  inversely  proportional  to  the  angle  i  of  normal  flight. 
From  this  point  of  view,  it  would  be  convenient  to  fly  with 
high  angles  of  incidence;  this,  however,  is  not  possible,  for 
reasons  which  shall  be  presented  later. 


FLYING  IN  THE  WIND  159 

Let  US  now  suppose  that  the  gust  be  such  as  to  make  the 
direction  of  the  relative  wind  depart  from  the  plane  of 
symmetry;  there  will  then  be  an  angle  of  drift.  A  force  of 
drift  will  be  produced,  and  if  the  airplane  is  stable  in  calm 
air,  a  couple  will  be  produced  tending  to  put  the  airplane 
against  the  wind  and  to  bank  it  on  the  side  opposite  to  that 
from  which  the  gust  comes.  Naturally  it  is  necessary  that 
these  phenomena  be  not  too  accentuated  in  order  not  to 
make  the  flight  difficult  and  dangerous  with  the  wind  across. 
We  find  here  the  confirmation  of  the  statement  that  stabiliz- 
ing couples  be  not  excessive. 


PART  III 

THE  EFFICIENCY  OF  THE  AEROPLANE 


CHAPTER  XII 

PROBLEMS  OF  EFFICIENCY 

Factors  of  Efficiency  and  Total  Efficiency 

The  efficiency  of  a  machine  is  measured  by  the  ratio  be- 
tween the  work  expended  in  making  it  function  and  the 
useful  work  it  is  capable  of  furnishing.  For  a  series  of 
machines  and  mechanisms  which  successively  transform 
work,  the  whole  efficiency  (that  is,  the  ratio  between  the 
energy  furnished  to  the  first  machine  or  mechanism  and 
the  useful  energy  given  by  the  last  machine  or  mechanism), 
is  equal  to  the  product  of  the  partial  efficiencies  of  the 
successive  transformations. 

To  be  able  to  effect  the  calculation  of  efficiency  in  an 
airplane,  it  is  necessary  to  consider  two  principal  groups  of 
apparatus:  the  engine-propeller  group  and  the  sustenta- 
tion  group.  There  is  no  doubt  of  the  significance  of  the 
engine-propeller  group  efficiency;  it  is  the  ratio  between  the 
useful  power  given  by  the  propeller  and  the  total  power 
supplied  to  it  by  the  engine.  The  sustentation  group 
comprises  the  wings,  the  controlling  surfaces,  the  fuselage, 
the  landing  gear,  etc.;  that  is,  the  mass  of  apparatus  which 
forms  the  actual  airplane. 

For  the  sustentation  group,  the  efficiency,  as  it  was  pre- 
viously defined,  has  no  significance,  because  neither  sup- 
plied energy  nor  returned  energy  is  found  in  it.  The 
function  of  the  sustentation  group  is  to  insure  the  lifting 
of  the  airplane  weight,  with  a  head  resistance  notably  less 
than  the  weight  itself      The  ratio  between  the  lifted  weight 

161 


162  AIRPLANE  DESIGN  AND  CONSTRUCTION 

and  the  head  resistance  is  usually  taken  as  the  measure  of 
the  efficiency  of  the  sustentation  group. 

The  hfted  load  of  an  airplane  is  given  by  the  expression 

L  =  10-"  XA72 

and  the  head  resistance  is  equal  to  the  sum  of  two  terms; 
one  referring  to  the  wing  surface,  the  other  to  the  parasite 
resistances : 

D  -  10-'  (5.4  +<x)V' 

Thus  the  efficiency  of  the  sustaining  surface  can  be 
measured  by 

_  L^-       ^^ 
^  ~  D~  8A  +  a 

If  p  is  the  propeller  efficiency,  the  product  r  =  p  X  e  can 
serve  well  enough  to  characterize  the  total  efficiency  of  the 
airplane.  Naturally  the  number  r  cannot  be  considered  as 
a  ratio  between  two  works;  and  it  differs  from  a  true  and 
proper  efficiency  (which  is  always  smaller  than  unity)  because 
it  is  in  general  greater  than  unity,  as  it  contains  the  factor 
e  which  is  always  greater  than  1.  Let  us  immediately 
note  that  the  value  of  r  is  not  constant,  because  the  values 
of  e  and  p  are  not  constant.  In  fact  e  is  a  function  of  X 
and  8,  which  vary  with  the  variation  of  the  angle  of  inci- 
dence i,  and  p  is  a  function  of  the  speed  V  and  of  the  number 
of  revolutions  n  of  the  engine.  Practically,  it  is  interesting 
to  know  the  value  of  r  as  a  function  of  the  speed,  which  is 
possible  by  remembering  the  equation 

W  =  L  ^  10-^  \AV^ 

In  fact  W  being  constant,  this  equation  permits  the  deter- 
mining of  a  corresponding  value  V  for  each  value  of  i,  and 
therefore  the  making  of  a  diagram  of  efficiency  e  as  a  func- 
tion of  speed  V.  Moreover,  by  what  has  already  been 
mentioned  in  Chapter  IX,  when  the  engine  propeller  group 
is  fixed,  the  value  of  p  as  a  function  of  V  can  be  found  and 
then  it  is  easy  to  draw  the  diagram  of  r  as  a  function  of  V. 


PROBLEMS  OF  EFFICIENCY 


163 


It  is  possible  to  give  r  a  much  simpler  expression  than 
the  preceding  one;  thus 

r  =  p  X 


8A  -\-  a 

obtaining  \A  and  {8 A  +  o-)  from  the  equations 
W  =  10-'\AV' 
550Pi  =  1.47  10-'*  {8A  +a)V^ 

and  substituting  in  (1)  we  have 

WV 


0.00267p 


Pi 


(1) 


(2) 


Knowing  W,  the  diagrams  p  =  f{V)  and  Pi  =  /(F),  we 
can  draw  the  diagram  r  =  f{V). 


A 

0 

^ 

Ns 

/ 

N 

/ 

S 

s 

s 

K 

§ 

v 

^ 

=.^ 

^ 

^ 

■ 

._ 

_J 

L_j 

0       70      50      90       100      110      120      130      W      60     160 

V 

Fig.   109. 

Let  us  draw,  for  instance,  this  diagram  for  the  airplane 
of  the  example  of  Chapter  IX.  For  this  airplane  we  have 
W  =  2700  lb.,  consequently 

V 


7.2p 


Pi 


Fig.  93  gives  the  values  of  Pi  and  p  corresponding  to  the 
various  speeds  for  the  propeller  which  has  already  been  con- 
sidered in  Chapter  IX.  We  can  then  obtain  the  value  of  r 
corresponding  to  each  value  of  V  and  draw  the  diagram  of 
Fig.  109. 


164  AIRPLANE  DESIGN  AND  CONSTRUCTION 

This  diagram  shows  that  r  is  maximum  and  equal  to  6.9 
for  a  value  of  speed,  V  =  95  m.p.h.,  after  which  it  decreases; 
for  V  =  160  m.p.h.  for  instance  (which  represents  the  maxi- 
mum speed  of  the  airplane  under  consideration)  r  =  3.12; 
that  is  r  is  equal  to  51  per  cent,  of  the  maximum  value.  In 
other  words  our  airplane  running  at  its  maximum  speed, 
has  an  efficiency  equal  to  about  one-half  the  efficiency  it 
has  at  the  speed  of  95  m.p.h.  to  which  corresponds  to  the 
maximum  climbing  speed. 

Let  us  consider  again  formula  (2) ;  since  Pi  =  pP2  when 
the  airplane  flies  horizontally  at  its  maximum  speed,  equa- 
tion (2)  can  also  be  written 

W  V  V 
r  =  0.00267  X       ^ 

Practically  then  when  we  know  the  maximum  speed  of 
the  airplane  and  the  corresponding  maximum  power  of  the 
engine,  it  is  possible  to  have  the  value  of  r  corresponding 
to  the  maximum  speed. 

This  value  is  much  lower  than  the  maximum  which  the 
airplane  can  give;  thus  calculating  r  based  on  the  maxi- 
mum speed  of  the  airplane  and  on  the  maximum  power  of 
its  engine,  we  would  have  an  imperfect  idea  of  the  real 
total  efficiency. 

Now  w^e  intend  to  show  that  to  measure  the  efficiency 
corresponding  to  the  maximum  climbing  speed  is  not  a 
difficult  matter. 

Let  us  suppose  in  fact  that  the  airplane  makes  a  climbing 
test  and  let  n  be  the  number  of  revolutions  of  the  engine 
while  climbing.  Let  V  be  the  speed  of  translation  meas- 
ured by  one  of  the  usual  speedometers.  Knowing  n,  we 
know  the  value  P'2  corresponding  to  the  power  developed 
by  the  engine. 

Such  power  is  absorbed  partly  by  the  airplane,  and  partly 
by  the  work  necessary  to  do  the  lifting.  Let  y^ax.  be  the 
maximum  climbing  speed,  which  can  be  measured  by  ordi- 
nary barographs.     The  power  absorbed  by  flying  will  be 

Wv 

nf    __     ''  ''max. 

'       T50p' 


PROBLEMS  OF  EFFICIENCY  165 

where  p'  is  the  propeller  efficiency  which  can  be  estimated 

7' 
with  sufficient  approximation  knowing  — ^  {V  is  the  hori- 
zontal speed  corresponding  to  y^ax.)- 
We  then  have 

V'W 


2 


550p' 

that  is,  by  measuring  Y' ,  v  and  n,  and  by  estimating  p  ,  it 
is  possible  to  have  a  value  approximate  enough  to  the  maxi- 
mum value  of  the  total  efficiency.  Breguet  has  proposed 
an  expression  which  he  calls  motive  quality,  whose  magnitude 
can  be  used  to  give  an  idea  of  the  efficiency  of  the  airplane. 
Let  us  remember  the  two  equations 

W  =  lO-'xAV 
pP2  =  0.267  10-6  {5A  +  a)V' 

By  eliminating  V  from  the  two  preceding  equations,  w^e 
have 

1      1    ^  +  i 

P2  =  0.267  Tr^  X  -^  XX ^  (3) 

■\/A        p  X 

The  motive  quality  q  is  the  expression 
q  =  p 


^  +  j 


Let  us  remember  that 

X^ 


We  see  that 

q  =  rVx 
That  is,  q  is  proportional  to  r  and  therefore  it  measures  the 
efficiency  of  the  airplane. 
Equation  (3)  can  be  written 

P,  =  0.267  —Z- 


VAXq 


16G  AIRPLANE  DESIGN  AND  CONSTRUCTION 

from  which  we  have 

^  0.267  W^^ 

^         P,  VA 

Also  q  assumes  various  values,   and  its  maximum  value 
corresponds    to    the    maximum   of   ascending   speed    v^^^. 
That  is,  we  have  by  expressing  v^^^.  in  ft.  per  second  that 
^  0.267  W^'- 

'^^^        Va(p'..     ^^><^--^ 


550p' 
which  can  also  be  written 

Iw 


147,,^ 


p 


max. 


Since  -^  is  the  load  per  sq.  ft.  of  the  wing  surface,  and  ,^5 

is  the  weight  per  horsepower  of  the  airplane,  v^^^.  and  p'  being 

known,  ^max-  is  easily  calculated.     In  the  preceding  example 

we  have  for  instance 

W  P' 

IL.  =  10- €l  =  7.3;  i/  =  33;  p'  =  0.695 

A  yy 

consequently 

Qm...  =  0.117 


CHAPTER  XIII 
THE  SPEED 

In  ordinary  means  of  locomotion,  speed  is  usually  con- 
sidered as  a  luxury,  but  in  the  airplane,  it  represents  an 
essential  necessity,  for  the  whole  phenomenon  of  sustenta- 
tion  is  based  upon  the  relative  speed  of  the  wing  surfaces 
with  respect  to  the  surrounding  air. 

The  future  of  the  airplane,  as  to  its  application  in  every- 
day life,  stands  essentially  upon  its  possibility  of  reaching 
average  commercial  speeds  far  superior  to  those  of  the  most 
rapid  means  of  transportation. 

When  the  airplane  is  in  flight,  high  speeds  present  dangers 
incommensurably  smaller  than  those  which  threaten  a 
train  or  a  motor  car  running  at  high  speed.  On  the  con- 
trary we  have  seen  that  the  faster  an  airplane  is,  the  better 
it  fights  against  the  wind.  It  is  quite  true  that  high  speeds 
present  real  dangers  when  landing,  but  modern  speedy 
airplanes  are  designed  so  as  to  permit  a  strong  reduction 
in  speed  when  they  must  return  to  earth. 

Let  us  remember  that  the  two  general  equations  of  the 
flight  of  an  airplane  are: 

W  =  10-^  \AV^  (1) 

550p  X  P2  =  1.47  10-^  {6A  +  <t)V'  (2) 

by  expressing  Po  in  H.P.  and  V  in  m.p.h.     Equation  (2) 
gives, 

Ji  p  H 

We  see  then,  that  if  we  wish  to  increase  V  we  must  increase 
p  and  P2,  decrease  8,  A  and  a. 

The  improvement  of  p  is  of  the  greatest  importance  not 
only  in  order  to  obtain  a  higher  speed  but  also  in  order  to 
improve  the  total  efficiency.     In  regard  to  propellers,  we 

167 


168  AIRPLANE  DESIGN  AND  CONSTRUCTION 

have  discussed  their  efficiency  and  the  factors  which  have 
influence  upon  it,  and  we  have  seen  that  p  is  a  function  of 

the  ratio  — ^■ 
irnD 

V 
By  drawing  the  diagram  p  as  a  function  of  — ^,  we   see 

that  p  passes  through  a  maximum  value  p„,^^.  after  which  it 
decreases. 

The  value — ^  (to  which  the  vahie  p„,ax.  corresponds)  is 

directly  proportional  to  the  ratio  w^  •     Let  us  con- 

sider, for  instance,  three  propellers  of  diameter  /)',  D", 
D'"  and  of  pitch  p' ,  p",  p'"  such  that  p'/D'<v"/D"< 
p'" /D'"]  the  curves  of  the  efficiencies  p',  p" ,  p"  will  be 
such  that  p'max.j  p"max->  ^"^^  p'"max-  corrcspoud  to  the  three 
Y'         Y"        Y'" 

values  — n  <  -^  <  — n  (^ig-  HO). 
tuD      irnD      irnD 

Now,  if  with  a  given  machine  we  wish  to  have  the  maxi- 
mum horizontal  speed,  it  is  convenient  to  select  the  pro- 
peller of  such  pitch  and  diameter  so  as  to  give  the  maximum 
efficiency  at  that  speed.  In  formula  (3),  the  propeller 
efficiency  is  seen  to  be  to  the  %  power;  this  means  that  for 
each  1  per  cent,  of  increase  of  the  efficiency,  the  speed 
increases  only  by  }yi  per  cent. 

The  increase  of  the  motive  power  P2  is  another  means  of 
increasing  the  speed;  alsoP2  is  seen  to  be  to  the  %  power  and 
consequently  at  first  glance,  we  may  think  that  for  a  per- 
centual  increase  of  P2  the  same  may  be  applied  as  that  which 
has  been  said  for  a  per  cent,  increase  of  p.  Practically 
though,  to  increase  P2  means  adopting  an  engine  of  higher 
power,  consequently  of  greater  weight  and  difTerent 
incumbrance.  Thus  the  change  of  P2  is  reflected  upon  the 
terms  6  ,  A  and  c.  It  is  not  possible  to  translate  into  a 
formula  the  relation  which  exists  between  P2,  5,  A  and  <r. 
It  is  necessary  then  to  make  proper  verifications  for  each 
successive  case. 

The  value  of  5  depends  upon  the  form  and  profile  of  the 
wing  surface;  it  is  smaller  for  the  wings  with  very  flat 


THE  SPEED 


169 


170  AIRPLANE  DESIGN  AND  CONSTRUCTION 

aerofoil,  and  which  for  this  reason  are  usually  called  "wings 
for  speed. "  For  very  fast  machines,  some  designers  have 
even  adopted  wings  with  convex  instead  of  concave  bot- 
toms. Naturally  this  convexity  is  smaller  than  that  of 
the  wing  back  (Fig.  111).  We  then  also  have  a  negative 
pressure  below  the  bottom,  and  the  sustentation  is  then  due 
to  the  excess  of  negative  pressure  on  the  back  with  respect 
to  that  on  the  bottom. 

The  decrease  of  sustaining  surface  A  also  has  influence 
upon  the  increase  of  speed. 


Fio.   111. 

From  this  point  of  view  it  would  then  be  convenient  to 

W 
greatly  increase  the  load  per  unit  of  the  wing  surface  -j- 

But  remembering  equation  (1)  we  have  that 
7=100  Jf   X 

W 
This  expression  states  that  when  -^  is  given,  the  value  of 

V  is  inversely  proportional  to  VX- 

Let  us  give  X  the  maximum  value  X^ax.  which  it  is  practi- 
cally possible  to  give  (the  one  corresponding  to  i  =  8°  to 
10°) .  Then  the  preceding  formula  gives  the  minimum  value 
of  the  speed  it  is  possible  to  attain. 


z 


VXmax.      \A  \A 

that  is,  the  minimum  speed  at  which  the  airplane  can 
sustain  itself  is  directly  proportional  to  A~^-  Conse- 
quently if  we  wish  to  keep  the  value  of  F^in.  within 
reasonable    limits    of    safety,    it    is   necessary  not    to  ex- 

W 
cessively  increase  the  value  of    ^  '  ^^^^^^'   ^'^^  ^^^^   ^^    ^^" 


THE  SPEED  171 

cessively  reduce    the  value  of  A.     Practically    the   value 

W 

of  -T-  is  kept  between  6  and  10  lb.  per  sq.  ft. 

For  the  sake  of  interest  we  shall  recall  that  in  the  Gordon 

Bennett  race  of  1913,  machines  participated  with  a  unit 

load  up  to  13  lb.  per  sq.  ft.     Such   machines  are  difficult 

to  maneuver;  are  the  worst  gliders,  and  naturally  require 

a    great   mastery   in   landing;    their   practical   use  would 

have  been  excessively  dangerous.     For  sport  and  touring 

W 
machines,  the  value  of  ^  must  be  lowered  to  values  of  6  to 

4  and  even  3  lb.  per  sq.  ft. 

The  decrease  of  <r,  analogous  to  the  increase  of  p,  consti- 
tutes one  of  the  most  interesting  means  of  increasing  speed. 
Let  us  remember  that 

<x  =  ^  KA 

that  is,  it  is  equal  to  the  sum  of  all  the  passive  resistances 
due  to  the  various  parts  of  the  airplane.  For  decreasing 
c  it  is  then  necessary: 

1.  To  reduce  the  coefficients  of  head  resistance  of  the 
various  parts  to  a  minimum, 

2.  To  reduce  the  corresponding  major  sections  to  a 
minimum. 

In  order  that  the  reader  may  have  an  idea  of  the  influ- 
ence of  the  five  factors  p,  P^,  5,  A,  and  a  upon  the  speed, 
let  us  suppose  that  for  a  given  airplane  any  four  of  the 
above  terms  are  known,  and  let  us  see  how  V  varies 
with  a  variation  of  the  5th  element. 

Suppose  for  instance  that 
p  =  0.7; P2  =  350H.P.;5  =  0.6;^  =  340sq.  ft.;(r  =  200. 
Then,  giving  P2,  5,  A,  and  a  the  preceding  values,  let  us 
draw  the  diagram  of  the  equation 

V  =  155  P^350   ^^  ^^2). 

^0.6  X  340  -f  200 

By  making  5  vary  from  the  value  0.7  to  the  value  0.8, 
we  see  that  while  for  p  =  0.7,  the  speed  is  about  130 
m.p.h.;  for  p  =  0.8  it  is  above  136  m.p.h.;  that  is,  while  the 


172 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


efficiency  increases  by  14.3  per  cent.,  the  speed  increases 
by  4.6  per  cent. 

Analogously  the  diagram  T"  =  /(P2),  V  =  fid),  V  =  f(A), 
and    V  =  /(a),    have    been    drawn   respectively   in   Figs. 


0.70 


Q7Z 


\0'o 

/ 

T 

/ 

/ 

/ 

135 

/ 

/ 

/ 

/ 

J 

-% 

r 

\ 

^N 

J 

o': 

r 

A 

l/ 

-\ 

/ 

133 

/ 

/ 

' 

/ 

/ 

/ 

/ 

\JL 

> 

/ 

/ 

/ 

131 

/ 

> 

r-^ 

/ 

/ 

ion 

0.74  076 

P 

Fig.   112. 


0.7S 


0.50 


113, 114, 115,  and  IIG,  always  adopting  the  preceding  values 
for  the  constant  terms. 

All  the  foregoing  presupposes  the  air  density  constant 
and  equal  to  the  normal  density;  that  is,  to  the  one  corre- 


THE  SPEED 


173 


spending  to  the  pressure  of  33.9  ft.  of  water  and  to  the  tem- 
perature of  59°F. 

137r 


136 


135 


134 


> 


133 


132 


131 


I3Q 


, 

/ 

/ 

/ 

/ 

/ 

/ 

y 

/ 

/ 

/ 

^, 

/ 

,i/ 

^ 

,^ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

350 


360 


370  380 

PeHp. 


390 


400 


Now  as  it  is  known  tlie  density  of  the  air  decreases  as  we 
rise  in  the  atmosphere  (see  Chapter  V),  following  a  logarith- 
mic law  given  by  the  equation 

^^^  -  =  00720  log  1 


R 


60720  log  ^"X^^^"^*' 


(1) 


174 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Where  H  is  the  height  in  feet, 

Po    . 

p-  is  the  ratio  between  the  pressure  at  sea  level  and  the 

pressure  at  height  H; 

t"  is  the  Fahrenheit  temperature  at  sea  level,  and 

fi  is  the  ratio  between  the  density  at  height  H  and  the 

normal  density  defined  above. 

140 


133 


136 


134 


132 


I3a 


■ 

V 

\ 

\ 

s 

V 

\ 

\ 

\ 

N 

1 

\ 

\ 

^\ 

\ 

k^^ 

f^:^ 

1 

1 

s 

s?^ 

^^N 

\ 

1 

\ 

\ 

! 

1 

i\ 

s    1 

N 

\ 

\ 

S 

— 

— 

\ 

s. 

-N 

0,40 


0.44 


046  0.52 

u 
Fig.  114. 


0.5^ 


0.60 


Equation  (1)  can  be  translated  into  linear  diagrams  by 
using  a  paper  graduated  with  a  logarithmic  scale  on  the 
ordinates,  and  with  a  uniform  scale  on  the  abscissae,  giving 
to  t"  successively  various  values.  In  Fig.  117  these  lines 
are  drawn  for  t"  =  0°,  20°,  40°,  59°  and  80°F. 

By  using  these  diagrams,  the  density  corresponding  to 
a  given  height  for  a  given  value  of  the  temperature  at 
ground  level,  is  easily  found. 


THE  SPEED 


175 


Then  let  us  again  take  up  the  examination  of  the  formula 
for  speed 

F  =  155  X      '''^''' 


136 


■=    134 

a. 

E 


132 


128 


^                        T^ 

\ 

^ 

V 

\ 

V 

> 

\ 

4^X 

\^ 

\ 

V 

N 

S 

V 

\ 

5^ 

j^ 

^ 

\ 

200 


250  300 

A   3q  Pt-. 
Fig.   115. 


and  let  us  place  in  evidence  the  influence  of  the  variation  of 
the  density  on  various  parameters  which  appear  in  it. 

The  efficiency  p  is  a  function  of  ~^:  now  this  ratio  is 

nU 

influenced  by  the  variation  of  the  density,  since  V  and  n 

vary;  then  also  p  varies  with  a  variation  of  fj.. 

We  have  already  spoken  of  the  influence  of  the  density 


176 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


on  the  motive  power  in  Chapter  V,  where  we  saw  that  the 
ratio  between  the  power  at  height  H  and  that  at  ground 
level  is  equal  to  m- 


136 


135 


134 


133 


132 


J3I 


130 


\, 

N 

s 

\ 

w 

\ 

\ 

\ 

\, 

s 

s. 

\ 

J 

\ 

VQ 

\ 

?. 

\> 

> 

S, 

s 

S, 

\ 

s 

\ 

k. 

\ 

\ 

\ 

\, 

\, 

V 

\, 

\ 

V, 

s 

— 

150 


160 


ITO  180 

Fig.   IIG. 


190 


ZOQ 


The  useful  power  pP2  given  by  the  engine  propeller  group 
is  thus  a  function  of  the  air  density;  therefore  the  diagram 
P-P2  =  f{V)  changes  completely  with  a  variation  of  /x.  In 
Chapter  IX  we  saw  how  to  draw  that  diagram  when  the 
density  is  normal;  that  is,  ^  =  1.     Let  us  now  consider 


THE  SPEED 


177 


the  case  of  /^  <  1.     The  ratio  -~r-.  =  a  is  not  only  a  function 

V 
of  -^,  but  also  of  /x;  and  precisely  that  ratio  is  proportional 


25O0O 

H=e0120hgjj:=e07?0hg(^^  f;/^) 

\ 



\ 

\Mv" 

\ 

NK\\ 

S^r" 

20000 

^^ 

^^ 

S^S 

^Si^^ 

VC^s.*^V          -   

15000 

_^^XA 

^s^t 

5;£^s 

>^^3po 

lOOOO 

"vi^Vv 

ly  V\\ 

^saK\\ 

sT^^^ 

^o^^^ 

5000 

S\^  vn 

__.^_.VAa 

'^5\ 

^  M\ 

n 

■: ::::::::  mmr 

0.4  0.5  0.6        0.7      0.8     09      1.0    1.10  1.20 

Fig.   117. 


to    li..     Consequently    for    each    value    of    /x    a    diagram 


n'D' 


needs  to  be  drawn.     In  Fig.  118  such  diagrams  have 


been  drawn  on  a  logarithmic  scale  for  the  propeller  family 
to  which  Fig.  89  of  Chapter  IX  refers,  and  for  the  values  y.  = 


178 


AIRPLANE  DESIGX  AND  CONSTRUCTION 


1.0,  0.55,  0.41,  0.25,  corresponding,  for  a  temperature  of 
59°  R,  to  the  heights  of  0,  16,000,  24,000  and  28,000  ft. 

The  diagram  which  gives  the  motive  power  A  as  function 
of  the  number  of  revolutions  is  also  to  be  decreased  propor- 

r500 


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Fig.   118. 


tional  to  /x.  In  Fig.  119  we  have  taken  up  again  the 
diagram  of  Fig.  91  of  Chapter  IX,  drawing  it  for  the  preced- 
ing values  /i. 

Then  by  the  known  construction,  we  can  draw  the  dia- 
grams pPi  =  /(F)  for  the  preceding  values  of  m  (Fig.  120). 


THE  SPEED 


179 


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180 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


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THE  SPEED  181 

In  order  to  make  evident  the  influence  of  the  decrease 
of  the  air  density  on  the  parameter  proper  of  the  airplane, 
or  in  other  words  on  the  power  Pi  necessary  to  flying,  let 
us  take  up  again  the  general  equation  of  flight 

W  =  10~'\AV-' 
550Pi  =  1.47  X  10-4  (U  +  <r)  V 

and  make  evident  the  influence  of  the  air  density. 

We  have  seen  in  Chapter  VII  that  X,  8,  and  o-  vary  propor- 
tionally to  jj.;  consequently  the  preceding  equations  become 

W  =  10-'  ixXAV^- 
SoOPi  =  1.47  X  10-4  M  (dA  +  a-)  V 

that  is,  remembering  what  has  been  said  in  Chapters  VIII 
and  IX 

W 


and 


^V'"'' 


^m  =  1.47A 


Then  considerations  analogous  to  those  developed  in  the 
preceding  chapters  enable  us  to  take  fj,  into  account  by 
introducing  a  new  scale  with  a  slope  of  1/1  on  the  axis  of 
the  abscissae  and  to  pass  from  the  origin  to  any  point  what- 
soever of  the  diagram  by  summing  geometrically  four  seg- 
ments equal  and  parallel  to  W,  P,  V  and  /x. 

As  the  weight  of  the  airplane  is  constant  and  equal  to 
2700  lb.,  it  is  possible  according  to  what  has  been  said 
in  Chapter  IX,  to  simplify  the  interpretation  of  the  diagram, 
proceeding  as  follows: 

Let  us  consider  the  diagram 

A  =/(1.47  X  A) 

for  M  =  1  (Fig.  120).  From  each  point  of  this  diagram  let 
us  draw  segments  parallel  to  the  scale  of  fx  and  which  meas- 
ures to  this' scale,  the  value  /x  =  0.55.  Let  us  join  the 
ends  of  these  segments.  We  shall  have  a  new  diagram  A  =  / 
(1.47a)  corresponding  to  /i  =  0.55.     We  intend  to  demon- 


182  AIRPLANE  DESIGN  AND  CONSTRUCTION 

strate  that  if  from  any  point  whatsoever  A  of  this  diagram 
we  draw  a  parallel  to  the  scales  of  T^  and  P,  we  shall  have 
in  A'  and  A"  respectively  a  pair  of  corresponding  values 
of  speed  V  of  power  Pi  for  n  =  0.55,  that  is  at  the 
height  of  16,000  ft.  In  fact  let  us  call  A'"  the  meeting 
point  of  the  straight  line  A  A'"  drawn  parallel  to  the  scale 
of  /x,  on  the  original  diagram.  By  construction  A  A'"  is 
equal  to  0.55.  Let  us  suppose  now  that  we  wish  to  find 
the  corresponding  pairs  of  values  V  and  Pi  for  W  = 
2700  and  /x  =  0.55.  Then  it  will  be  sufficient  to  draw  from 
0'  corresponding  to  2700  lb.  a  parallel  to  the  scale  of 
power  and  from  A,  extreme  point  of  the  segment  A  A'" 
corresponding  to  the  value  /x  =  0.55  a  parallel  to  the  scale 
of  speed.  These  two  straight  lines  will  meet  in  A"  and 
will  individuate  two  segments  0'  A"  and  A  A"  as  measure 
of  the  corresponding  power  and  speed. 

Thus,  as  A  A"  =  0"A',  if  we  wish  to  study  the  flight  at 
a  height  of  16,000  ft.,  it  is  possible  to  use  the  diagram  A  =  / 
(1.47a)  drawn,  by  adopting  the  same  scales  as  said  above. 

Based  upon  analogous  considerations  the  diagrams  A  = 
/(1.47a)  for  /i  =  0.41  and  ix  =  0.35,  have  been  drawn. 

We  then  dispose,  in  Fig.  120  of  four  pairs  of  diagrams, 
which  give  the  values  of  Pi  and  pP^  corresponding  to  m=  1; 
0.55;  0.41  and  0.35,  that  is,  for  the  heights  of  0,  16,000, 
24,000  and  28,000  ft.  The  meeting  points  of  these  dia- 
grams define  the  maximum  value  of  the  speed  which  the 
airplane  can  reach  with  that  given  engine-propeller  group 
at  the  various  heights.  The  diagrams  corresponding  to  the 
height  of  28,000  ft.  do  not  intersect.  This  means  that  for 
the  airplane  of  our  case  the  flight  would  not  be  possible 
at  this  height. 

For  the  lower  altitudes  it  is  possible  to  draw  the  diagrams 
of  the  corresponding  maximum  and  minimum  speeds  (Fig. 
121).  Let  us  note  immediately  that  while  the  maximum 
speeds  depend  essentially  upon  the  engine-propeller  group 
and  consequently  can  be  varied  with  a  variation  of  the 
characteristic  of  this  group  the  minimum  speeds  depend 
exclusively  upon  the  airplane.     From  the  examination  of 


THE  SPEED 


183 


the  diagrams  of  Fig.  120  we  see  that  as  we  raise  in  the 
atmosphere  the  maximum  speed  which  the  airplane  can 
reach  diminishes  gradually  while  the  minimum  flying  speed 
increases  accordingly. 

It  is  interesting  to  study  the  case  (merely  theoretical  at 
the  present  stage  of  the  technique  of  the  engines)  in  which 


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the  motive  power  is  not  effected  by  the  variation  of  the  air 
density  but  keeps  constant  at  the  various  heights.  We 
shall  see  immediately  that  in  this  case  the  propeller  wiU 
greatly  increase  the  number  of  revolutions;  it  is  then  nec- 
essary to  extend  the  characteristics  of  the  engine  above 
2200  revolutions  per  minute. 

Let  us  suppose  that   this   characteristic   be  the  one  of 
Fig.  122 -.     We  can  then  draw  by  the  usual  construction  the 


184 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


550 
-500 
•450 
-400 
•350 
-300 

•250 
-200 

-150 


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1-50 


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Fig.  122. 


THE  SPEED 


185 


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186 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


pairs  of  corresponding  diagram,  which   give  Pi  and   pPz. 
This  has  been  done  in  Fig.  123,  in  which  has  been  drawn 


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only  part  of  the  diagrams  containing   the  intersections 
which  define  the  maximum  speeds.     We  see  how  these 


THE  SPEED  187 

speeds  vary,  as  they  increase  and  how  flight  becomes  pos- 
sible even  at  28,000  ft.  and  for  greater  altitudes.  For  our 
example  we  find  that  the  speed  at  28,000  ft.  is  equal  to 
265  m.p.h.,  while  at  sea  level  it  was  160  m.p.h.  Thus  we 
also  find  that  the  number  of  revolutions  of  the  propeller  at 
28,000  ft.  is  of  2450  r.p.m.  against  1500  r.p.m.  at  sea  level. 

Let  us  note  first  of  all  that  in  practice  it  would  not  be 
possible  to  run  the  engine  at  2450  r.p.m.  without  risking 
or  breaking  it  to  pieces,  if  the  engine  is  designed  for  a  maxi- 
mum speed  of  say  1800  r.p.m. 

In  second  place  we  shall  note  that  it  would  be  practically 
impossible  to  build  an  engine  or  a  special  device  such  as  to 
keep  the  same  power  at  any  height  whatsoever. 

The  utmost  we  can  suppose  is  that  the  power  is  kept  con- 
stant for  instance  up  to  12,000  ft.,  after  which  it  will  natu- 
rally begin  to  decrease  again.  In  order  to  make  a  more 
likely  hypothesis,  we  shall  suppose  that  the  power  is  kept 
constant  up  to  12,000  ft.  and  then  decreases  following  the 
usual  law  of  proportionality. 

Based  on  this  hypothesis  we  have  drawn  the  diagram 
of  Fig.  124  for  the  values 

M  =  1.00;  0.64;  0.55;  0.41;  0.35 

We  see  then  that  as  we  raise,  the  speed  increases  but  much 
less  than  in  the  preceding  case;  furthermore  after  12,000 
ft.  the  speed  remains  about  constant. 

If  we  could  build  propellers  with  diameter  and  pitch 
variable  in  flight,  the  operation  of  the  engine-propeller 
group  would  be  greatly  improved  and  a  great  step  would 
be  made  toward  the  solution  of  the  aviation  engine  for 
high  altitudes,  because  the  problem  of  propeller  is  one  of  the 
most  serious  obstacles  to  be  overcome  for  the  study  of  the 
devices  which  make  it  possible  to  feed  the  engine  with  air 
at  normal  pressure  at  least  up  to  a  certain  altitude. 


CHAPTER  XIV 


THE  CLIMBING 

In  Chapter  IX  we  have  seen  that  the  chmbing  speed  can 
be  easily  calculated  as  a  function  of  V,  when  the  power 
p  X  P2  furnished  by  the  propeller  and  the  power  Pi  neces- 
sary for  the  sustentation  of  the  airplane  at  that  speed,  are 
known;  and  we  have  seen  that  the  climbing  speed  v  (ex- 
pressed in  feet  per  second),  is  given  by 

pP2  -Pi 


V  =  550 


W 


L^ 


R.f(V) 


Pa-f(V) 


Fig.   125. 


Practically,  the  maximum  value  v^^^_  of  the  climbing 
speed,  obtained  when  the  difference  pPo  —  Pi  is  maximum, 
is  of  interest  to  us 

ipP2  —  Pi)  max. 


=  550 


W 


(la) 


Thus  if  we  wish  to  increase  the  climbing  speed  it  is  neces- 
sary to  make  the  value  {pP2  —  -fOmax.  the  maximum  possible. 

Let  us  suppose  that  the  power  P2  be  given ;  then  first  of 
all  it  is  necessary  that  the  airplane  be  built  so  that  the  mini- 
mum value  of  Pi  be  the  lowest  possible ;  in  the  second  place 
it  is  necessary  that  the  propeller  be  selected  so  as  to  give 

188 


THE  CLIMBING  189 

the  maximum  efficiency,  not  at  the  maximum  speed  of  the 
airplane,  but  at  lower  speeds,  in  order  to  increase  the 
difTerence  pPo  —Pi. 

Fig.  125  shows  how  this  can  be  accomplished;  the 
diagrams  p  and  p"  correspond  to  two  propellers  having 
different  ratio  v/D.  While  the  propeller  p  is  better  for  speed 
than  p",  the  propeller  which  corresponds  to  the  lower  value 
of  p/P  is  decidedly  better  for  climbing. 

Thus,  practically,  it  is  possible  to  adopt  an  entire  series 
of  propellers  on  a  machine,  to  each  one  of  which  corresponds 
two  special  values  for  the  maximum  horizontal  and  climbing 
speeds.  Naturally  the  selection  of  the  propeller  will 
be  made  according  to  whether  preference  is  given  to  the 
horizontal  speed  or  to  the  climbing  speed. 

In  order  to  study  in  full  details,  the  climbing  of  an  air- 
plane in  the  atmosphere,  it  is  necessary  to  study  the  influ- 
ence the  decrease  of  the  air  density  has  upon  the  climbing 
speed. 

Let  us,  as  before,  call  ju  the  ratio  between  the  air  density 
at  height  H,  and  at  sea  level.  At  sea  level  m  =  1  and  the 
maximum  climbing  speed  is  the  one  given  by  formula  (la). 

As  the  airplane  rises,  the  value  /x  decreases  and  then 
formula  (1)  should  be  written 

^max.    =  /(m) 

Referring  to  what  has  been  said  in  the  preceding  Chap- 
ter when  the  characteristics  of  the  airplane  for  ;u  =  1  are 
known,  it  is  easy  to  draw  for  different  values  of  p.,  the  curves 

pP,  = /(F)  and  Pi  =/(F) 

In  Fig.  120  of  the  preceding  chapter  we  have  drawn 
these  curves  for  the  example  of  Chapter  IX,  and  for  values  of 

p.  =  1.0,  0.55,  0.41 

For  convenience,  these  curves  are  reproduced  in  Fig.  126. 

Comparing   the   pairs   of   curves   corresponding   to   the 

same  value  of  p.,  it  is  easy  to  plot  the  diagram  which  gives 


190 


AIIWLANE  DESIGN  AND   CONSTRUCTION 


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2=1 


THE  CLIMBING 


191 


the  climbing  speed  at  the  various  heights.  In  Fig.  127  we 
have  drawn  this  diagram,  taking  ?'n,ax.  as  abscissae  and  H 
as  ordinates. 

It  is  interesting  to  draw  the  diagram 

t  =  f{H) 


', 


£0  30 

-if(max)-ft.perseo. 
Fig.  127. 


giving  the  time  spent  by  the  airplane  in  reaching  a  certain 
height  H.  To  construct  this  diagram  it  is  necessary  first  of 
all  to  draw  the  diagram  of  the  equation 

^  =  f(H),  Fig.  128a, 


which  is  easily  obtained,  from 

V  =  f{H) 


192  AIRPLANE  DESIGN  AND  CONSTRUCTION 


~ 

~ 

~ 

1 

) 

to=  59°F. 

!/ 

/ 

;  / 

/  [ 

' 

/ 

1 

/ 

j 

/ 

1 

/ 

1 

/ 

^ 

^ 

^ 

*  1 
V 

AH 

- 

- 

- 

-^ 

— 

— 

^- 

L 

■9. 

1 

0  6000  12000  l&OOO  £4000 

H(F+.) 

a 


0 

lO     1000 


7 

r 

7 

t 

y 

t 

7 

r 

Tp    a»  r                      -^ 

/_ 

^ 

y 

-.^^ 

^^            ^ 

^^                |1^ 

_^^  ** 

-e-'''''                                                                '' 

0  6000  12000  laoOO  24000 

H(Ft) 

b 

FlQ.   128. 


THE  CLIMBING  193 

By  integrating-  =  f{H)  we  have  t  =  f{H),  (Fig.  128  b). 

In  fact  the  elementary  area  of  the  diagram  -   =  f{H)  is 
equal  to 

but 

consequently 
and 


-XdH 

V 


dH 


X  dH  =  dt 


n 


X  dH  =  t 


that  is,  the  integration  of  diagram      =  f{H)  gives  t. 

In  Fig.  128  a,  b,  we  have  drawn  the  scales  of  H  ior  t  = 
59°.     Since  by  increasing  H   the   value  v  tends  toward 

zero,  that  of  -  tends  toward  <» ,  and  consequently  that  of  t 

also  tends  toward  0° .  That  is  to  say,  when  the  airplane 
reaches  a  certain  height,  it  no  longer  rises.  It  is  said  then, 
that  the  airplane  has  reached  its  ceiling. 

In  actual  practice  the  time  of  climbing  is  measured  by 
means  of  a  registering  barograph.  In  Fig.  129  an  example 
of  a  barographic  chart  has  been  given.  This  chart  gives 
directly  the  diagram 

H  =  m 

that  is,  it  gives  the  times  on  the  abscissae  and  the  heights 
on  the  ordinates.  Since  to  reach  its  ceiling,  the  airplane 
would  take  an  infinitely  long  time,  practically  the 
ceiling  is  usually  defined  as  the  height  at  which  the 
ascending  speed  becomes  less  than  100  ft.  per  minute. 

It  is  advisable  to  stop  a  little  longer  in  studying  the 
influence  the  various  elements  of  the  airplane  have  upon 
the  ceiling. 


194 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


THE  CLIMBING  195 

Let  US  again  consider  the  formula 

.  =  550  X  ^,,^ 
W 

and  let  us  place  in  evidence  the  influence  of  ^  on  the  differ- 
ence pP^  —  Pi. 

Supposing  that  we  adopt  a  propeller  best  for  climbing; 
that  is,  one  which  gives  the  maximum  efficiency  correspond- 
ing to  the  maximum  ascending  speed,  we  can,  with  sufficient 
practical  approximation,  assume  p  constant;  then,  since  P2 
varies  proportionally  to  m,  the  useful  power  available,  can 
be  represented  by 

MP-P2 
As  for  Pi, 

55OP1  =  1.47  X  10-4  {8 A  +  (t)V' 
but 

W  =  IO-UA72 

thus  eliminating  V  from  the  two  preceding  equations 

\^A^ 
Now  5,  0-,  and  X  are  proportional  to  m,  therefore 


Pi  =  267  X  10-3  {8A  +  (t)  X 

md  X  are  proportional  to  m, 
Pi   =   267   X    10-3(m5A   +  m^) 


=  267  X  10-3  i  (5A  -\-  a)  — ^^ 


and  we  can   then   write 

.=  f  [..A-267X10-3-l=(M+.)^-] 

Since  the  ceiling  is  reached  when  y  =  0,  it  will  correspond 
to  value  m',  w^hich  makes  the  second  term  of  the  preceding 
equation  equal  to  zero. 

267X10-3    ,,    ,     ,    TF?^ 


That  is 


m'pP2 ^j=^  {8A  +  c)  -I^  =  0 


,       267^^  X  10-^,,   ,     .,,W 


196  AIRPLANE  DESIGN  AND  CONSTRUCTION 

Remembering  that 

H  =  60,720  log  ^^ 

the  maximum  vaUie  //max.  of  ceiUiig  will  be 


that  is 


//max.  =  60,720  X  log  i 


//„„.  =  60,720  log  ^-^-^™,_^         (1) 


We  can  then  enunciate  the  following  general  principles: 

1.  Every  increase  of  p,  Po,  and  X.4  increases  the  ceiling  of 
the  airplane  and  vice  versa. 

2.  Every   decrease  of   8A,  <r,  and  W  similarly  increases 
the  ceiling  and  vice  versa. 

Equation  (1)  can  also  be  put  into  the  following  form: 

//^a..  =  60,720  log  ,,,,.,,,.,    .     xfww.H (2) 


(-jX^f(-p... 


\FiJ    \     A      J    \AJ 
where 


p  =  propeller  efficiency 

X  =  lift  coefficient  of  wing  surface 

W 

n"  =  weight  lifted  per  horsepower 

X    2 

J, —  =  total   resistance   per   square  foot  of  wing 

surface. 

W 

-J  =  load  per  square  foot  of  wing  surface. 

We  then  have  five  well-determined  physical  quantities 
which  influence  the  value  //max.-  As  an  example,  and  with 
a  proceeding  analogous  to  that  adopted  for  the  study  of 
horizontal  speed,  we  shall  give  to  these  parameters  a  series 
of  values,  and  then,  making  them  variable  one  by  one,  we 
shall  study  the  influence  of  this  variation  upon  //max.- 


THE  CLIMBING 


197 


Let  us  suppose  for  instance  that 

p  =  0.8;  X  =  22 

W 

^  =  6  lb.  per  H.P. 

^2 


8A  + 


1.2 


W 


61b.  per  sq.ft. 


35000 


34000 


33000 


32000, 


.....       «,„„,. _r,.",       220X2.41 

1 

/ 

'""■■        ""'-"'"'^L'     3.31X1.13X3.31 

J 

/ 

/ 

1 

/ 

/ 

/ 

/ 

J 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

y 

/ 

/ 

QTQ        0.72         0.74         07  0.78         0.80 

? 

Fig.  130. 


198 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Then  it  is  easy  to  draw  the  following  diagrams  on  a  paper 
having  the  logarithmic  graduation  on  the  axis  of  the  ab- 
scissae OX,  and  the  normal  graduation  on  the  axis  OY: 


0.8  X  2.41 


JiUVW 

y 

/ 

30000 

/ 

/ 

/ 

/ 

26000 

/ 

/ 

-(- 

/ 

^ 

/ 

E  zeooo 

31 

/ 

/ 

/ 

/ 

/ 

/ 

18000 

/ 

f 

/ 

J 

/ 

/ 

14000 

/ 

/ 

/ 

/ 

(nnnn 

18        20 


11 


FiQ.   131. 


=  /(p)  for  p  variable  from  0.7  to  0.8  (Fig.  130) 
=  /(X)  for  X  variable  from  10  to  22  (Fig.  131) 

/W\        W 
=  /( p- )  for  p-  variable  from  6  to  14  lb.  per  H.P. 

(Fig.  132)   ' 


THE  CLIMBING 


199 


H„„.  =/(^^')  for^2<^  variable  from   1.2 

to  1.8  (Fig.  133) 
■ffmax.  ^  /( ^ )  ^°^  ^  variable  from  6  to  9  lb.  per  sq.  ft. 

(Fig.  134) 


0^\J\} 

3Z00 

\ 

r       OS  X  22  0  ^  2.41        ,   """ 
^"'-="''^4(.-P=)3X1.13X3.3j_ 

- 

\ 

3000 

\ 

\ 

Z800 

\ 

\ 

\ 

s 

\ 

s^ 

\ 

s. 

2400 

s 

s. 

s 

\, 

2200 

\ 

N 

7000 

N 

\^ 

\ 

1800 

\ 

s 

\mo 

6  7  8  9         10        II        12      13     14 

W/ 

Fig.   132. 

We  wish  to  show  now,  how,  with  sufficient  practical  ap- 
proximation, it  is  possible  to  reduce  the  formula  which 
gives  i/max.j  to  become  solely  a  function  of  W,  P2  and  A ; 
that  is,  of  the  three  elements  which  are  always  known  in  an 
airplane.     In  fact  the  values  of  p  and  Xn^^x.  for  the  greatest 


200 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


parts  of  the  airplanes  are  values  differing  but  little  from 
each  other  and  which  can  be  considered  with  sufficient 
approximation  equal  to 

p  =  0.75         X  =  16 


//  moi  =  60720  log 


r         0.8  X  22.0  X  2.41         "I 
|^33.1X('A+5)JX3.31J 


^iVW 

32000 

\ 

\ 

\ 

31000 

\ 

\ 

30000 

N 

\ 

N 

\ 

g   29000 
E 

T* 

\ 

\ 

28000 

\ 

\ 

27000 

\ 

\ 

\ 

Z6000 

\ 

\ 

N 

\ 

?p,nnn 

> 

1.2 


1.4  1.5 

5A-t-(r 

A 
Fig.   133. 


1:7 


Let  us  furthermore  remember  that  the  head  resistance 
Rg  and  sustaining  force  R^  are  expressed  by 
Rs  =  10-' {^ A  +a)V^ 

R.  =  lo-^x^y^ 


THE  CLIMBING 


201 


and  consequently 


Rl  \A 


33000 


32000 


31000 


30000 


o  29000 
E 

2: 


28000 


27000 


26000 


25000 


6.0 


6.5 


7.0           75 

&.0 

8.5 

9.0 

W 
A 

Fig.  134. 

Now,  in  a  well-constructed  airplane,  the  minimum  value 
of  —    is  between  0.15  and  0.18.     Assuming  0.15,  we  shall 

have 

5A  +  <r 


\A 


=  0.15 


202  Aim'LAXE  DESIGN  AND  CONSTRUCTION 

and  for  X  =  10 


5A  +_ 
A 


=  2.4 


"™-^™'°9[-(#f|^] 


II       12      15      14     15    16    17   18   19  20 

Fig.  135. 


Then  formula  (2)  becomes 


H, 


60,720,  log 


0.75^^-  X  16  X  10^^ 
(EV  2.*'  m"  267. 


"(t) 


THE  CLIMBING  203 

that  is 

i^max.  =  60,720  log  ^^'^^ 


Based  on  this  formula,  we  have  plotted  the  diagrams  of 
Fig.  135  which  makes  it  possible  to  find  H^^^  rapidly  and 
with  sufficient  practical  approximation  when  the  weight, 
power  and  sustaining  surface  of  the  airplane  are  known. 


CHAPTER  XV 
GREAT  LOADS  AND  LONG  FLIGHTS 

In  studying  the  history  of  aviation,  the  continuous  in- 
crease of  the  dimensions  of  airplanes  and  of  the  power  of 
engines,  is  decidedly  marked.  From  the  small  units  of  30 
to  40  H.P.  with  which  aviation  started,  we  have  to-day  at- 
tained engines  v.hich  develop  600  H.P.  and  more. 

It  is  interesting  to  transfer  to  a  diagram  the  history  of 
the  increase  of  the  power  of  the  engines  from  1909  to  the 
end  of  1918,  that  is  the  progress  of  aviation  engines  in  9 
years  (Fig.  136). 


IW 

500 

/ 

500 

/ 

/ 

'400 

/ 

/ 

300 

/ 

y 

200 

^ 

-^ 

100 

- 

1 

— - 

— 

n 

H 

— 

-1 

— 

— ■ 

'1909      1910 


1911 


1912 


1913         1914 
Year 
Fig.    136. 


I9I& 


1917 


19ia        1913 


The  great  war  which  has  just  ended,  while  it  gave  a 
great  impulse  to  many  problems  of  aviation,  has  demanded 
that  the  high  power  available  should  be  almost  exclusively 
employed  in  raising  the  horizontal  and  ascending  speeds 
under  the  urgency  of  military  needs,  leaving  as  secondary 
the  research  of  great  loads  and  great  cruising  radii,  incom- 
patible with  too  high  horizontal  and  climbing  speeds. 
We  then  find  military  machines,  single  seater  scout  planes, 
that  with  300  H.P.  can  barely  carry  a  total  load  of  600  lb. 

204 


GREAT  LOADS  AND  LONG  FLIGHTS  205 

(including  pilot,  gasoline  and  armament),  and  two  seater 
machines  that  with  400  H.P.  and  more  can  barely  carry 
a  total  useful  load  of  1300  lb. 

Now  certainly  it  is  not  by  carrying  some  hundred  pounds 
of  useful  load  and  by  having  the  possibility  of  covering  two 
or  three  hundred  miles  without  stopping,  that  the  airplane 
will  be  able  to  make  its  entrance  among  the  practical  means 
of  locomotion.  It  is  necessary  that  the  hundreds  of  pounds 
and  miles,  become  respectively  thousands.  To  be  able 
to  traverse  great  distances  of  land  and  sea  with  safety, 
carrying  a  load  such  as  to  make  these  crossings  commercial, 
is  the  great  future  of  mercantile  aviation. 

To-day  then,  the  vital  problems  of  aviation  are :  the  in- 
crease of  the  useful  load  and  the  increase  of  the  cruising 
radius. 

At  first  glance  one  may  think  that  the  two  problems 
coincide;  this  is  only  partially  true,  each  one  having  proper 
characteristics,  as  it  will  better  be  seen  in  the  following 
part  of  this  chapter. 

Let  us  start  with  the  examination  of  the  problem  of  useful 
load. 

Let  us  call  W  the  weight  of  the  airplane  and  U  the  useful 
load;  since  U  is  a  fraction  of  W  we  can  write 

U  =  uW 
where  u  is  na.turally  less  than  1. 

Remembering  the  expression  of  total  efficiency  of  the 
airplane 

WV 


we  can  also  write 


r  =  0.00267   ^ 


U  =  375u~Po 


That  equation  shows  that  in  order  to  increase  the  useful 

T 

load  it  is  necessary  to  increase  u,  the  ratio  y,    and  P2. 
(a)  The  coefficient  u  =  ^  gives  the  per  cent,  which  is 


206  AIRPLANE  DESIGN  AND  CONSTRUCTION 

represented  by  the  useful  load  with  respect  to  the  total 
weight  of  the  airplane.  I^et  us  consider  two  airplanes 
having  equal  dimensions  and  forms;  let  us  suppose  that 
the  weight  be  W  for  both,  and  the  useful  loads  instead  be 
different  and  equal  to  Ui  and  U2.  Then  we  shall  have 
respectively 

U2  =  u,W 

Let  us  further  suppose  that  the  engine  be  the  same  for 
both  au'planes,  and  that  its  weight  be  equal  to  e  X  W; 
then,  calling  ai  X  W  and  02  X  W,  the  weights  of  the  struc- 
ture, that  is,  the  weights  of  the  airplanes  properly  speaking 
considered  without  engine  and  without  useful  load,  we  will 
have 

W  =  u,W  +  eW  +  a,W 

W  =  U2W  +  eW  +  a^W 

and  subtracting  member  from  member 

Ux  —  Ui  =  ai  —  a\ 

That  is  to  say  if  Ui  >  u^^  Wx  shall  have  a-i  >  ai,  and  vice  versa; 
that  is,  if  the  useful  load  of  the  first  machine  is  greater  than 
that  of  the  second,  the  weight  of  its  structure  will  instead  be 
less.  Now  the  weight  of  the  structures,  if  the  airplanes 
are  studied  with  the  same  criterions  and  calculated  with 
the  same  method,  evidently  characterize  the  solidity  of  the 
machine;  and  in  that  case  the  airplane  having  a  lesser  weight 
of  structure,  also  has  a  smaller  factor  of  safety,  and  if  this 
is  under  the  given  limits,  it  ma}^  become  dangerous  to  use  it. 

Therefore,  it  is  undesirable  to  increase  the  value  oi  u  =  ,fr 

by  diminishing  the  solidity  of  a  machine. 

It  may  also  happen  that  two  machines  having  different 
weights  of  structure,  can  have  the  same  factor  of  safety, 
and  in  that  case,  the  machine  having  less  weight  of  structure 
is  better  calculated  and  designed  than  the  other.  The 
effort  of  the  designer  must  therefore  be  to  find  the  maximum 
possible  value  of  coefficient  u,  assigning  a  given  value  to  the 


GREAT  LOADS  AND  LONG  FLIGHTS 


207 


factor  of  safety  and  seeking  the  materials,  the  forms  and  the 
dispositions  of  various  parts  which  permit  obtaining  this 
coefficient  with  the  minimum  quantity  of  material,  that  is, 
with  minimum  weight.  In  modern  airplanes,  the  coeffi- 
cient u  varies  from  the  minimum  value  0.3  (which  we  have 
for  the  fastest  machines,  as  for  instance  the  military  scouts) , 
to  the  value  of  0.45  for  slow  machines. 

The  low  value  of  u  for  the  fastest  machines  depends  upon 
two  causes: 

1.  The  factor  of  safety,  necessary  for  very  fast  machines, 
must  be  greater  than  that  necessary  for  the  slow  ones,  there- 


.,                                                        1                                      .,.., 

:::::::::::::::::::::::::::::::::::;  ^^^::  ::::::::::::::::::::: 

;,^|5t_.,- 

:::::   ::  _::;::::::::::^^:  :i      i      li     :  :::::::::^s^             ::: 

-r  H         '                 '             r                iSvL 

: _       _    .^y'..- .  r- [     r  1-         -\ L _     ■ 

J^                                  HI     l'            1                                                    J 

yf^                                     ' 

^TiN                           '       ' 

:::::   y-.z-     -\-  --  i":--  -     ]      r      -+ : 

\Jr\          \          W                            '1 

J<1                Li 

Ml            H        1                              J        J 

Fig.  137. 


fore  the  value  of  coefficient  a  in  the  fast  machines  is 
greater  than  in  the  slow  ones,  with  a  consequent  reduction 
of  the  value  u. 

2.  A  fast  machine  having  the  same  power,  must  be  lighter 
than  a  slow  machine  (see  the  formula  of  total  efficiency). 
That  is  to  say,  the  importance  of  coefficient  e  increases,  and 
therefore  u  diminishes. 

(6)  In  Chapter  XII,  we  studied  coefficient  r  and  saw  that 

T 

it  was  a  function  of  Y .     Let  us  now  study  ratio  ^  ^"^^  ^^^ 

in  it  the  maximum  value  to  be  put  in  the  formula  of  useful 
load. 


208  AIRPLANE  DESIGN  AND  CONSTRUCTION 

Fig.  137  shows  the  diagram  r  =  f{V)  already  given  in 
Fig.  109  of  that  chapter.  The  diagram  refers  to  a  par- 
ticular example;  its  development,  however,  enables  making 
some  considerations  of  general  character.  From  origin  0 
let  us  draw  any  secant  whatever  to  the  diagram.  This,  in 
general,  will  be  cut  in  two  points  A'  and  A";  let  us  call  r' 
and  r"  the  values  of  efficiency  and  V  and  V"  the  values  of 
speeds  corresponding  to  these  points. 

Then  evidently 

r         r  , 

y,  =  yT,  =  tan  a 

T 

Since  we  seek  the  maximum  value  of  y>  in  order  to  have 

two  values  r^  and  Vo  such  that  their  ratios  will  be  the 
maximum  possible,  it  will  suffice  to  draw  tangent  t  from 
origin  0  to  point  Ao  of  the  diagram, 

To  . 

=  tana^ax. 

Therefore  infinite  pairs  of  speeds  V  and  V"  exist,  re- 
spectively greater  and  smaller  than  Vo,  which  individual- 

T 

ize  equal  values  of  ratio  y  ]  naturally  one  would  choose  only 

the  values  of  speed  V ,  which  are  greater. 

Practically  it  is  not  possible  to  adopt  the  maximum 

To 

t: 

fore  scarcely  sustain  itself;  it  is  then  necessary  to  choose  a 
lower  value  of  y-  and  corresponding  to  a  speed  V\>Vo. 

The  value  y^  must  be  inversely  proportional  to  the  height 

to  be  reached.     In  fact  the  equation 

WV 
r  =  0.00267  -^ 

r    .  W 

states  that  ^  is  proportional  to  ^--     Now  as  the  maxi- 

W 
mum  height  //max.  is  a  function  of  p->  consequently  it  is  also 

jt  2 
T 

a  function  of  y' 


GREAT  LOADS  AND  LONG  FLIGHTS  209 

(c)  We  treat  finally  the  problems  which  relate  to  the 
increase  of  power  P^. 

The  increase  of  motive  power  has  the  natm-al  consequence 
of  immediately  increasing  the  dimensions  of  the  airplane. 

The  question  naturally  arises,  ''up  to  what  limit  is  it 
possible  to  increase  the  dimensions  of  the  airplane?" 

First  of  all  it  is  necessary  to  confute  a  reasoning  false  in 
its  premises  and  therefore  in  its  conclusions,  sustained  by 
some  technical  men,  to  demonstrate  the  impossibility  of  an 
indefinite  increase  in  the  dimensions  of  the  airplane. 

The  reasoning  is  the  following: 
Consider  a  family  of  airplanes  geometrically  similar,  having 
the  same  coefficient  of  safety. 

In  order  that  this  be  so,  it  is  necessary  that  they  have  a 

W 
similar  value  for  the  unit  load  of  the  sustaining  surface  -^ , 

and  for  the  speed,  as  it  can  be  easily  demonstrated  by  virtue 
of  noted  principles  in  the  science  of  constructions.     Let  us 
furthermore   suppose  that  the  airplanes  have  the  same 
total  efficiency  r. 
Then,  as 

WV 

r  =  0.00267  %^ 

and  as  r  and  V  are  constant,  W  will  be  proportional  to  P2 ; 
that  is  the  total  weight  of  the  airplane  with  a  full  load  will 
be  proportional  to  the  power  of  the  engine 

W  =  vPo 

The  weight  of  structure  a  X  TF  of  airplanes  geometric- 
ally similar,  is  proportional  to  the  cube  of  the  linear  dimen- 
sions, which  is  equivalent  to  the  cube  of  the  square  root  of 
the  sustaining  surface;  then 

aW  =  a'A^^ 

W 

but  -T-  =  constant,  therefore  A  is  proportional  to  W  and 

consequently  we  may  write 

aW  =  a"W^ 


210  AIRPLANE  DESIGN  AND  CONSTRUCTION 

that  is 

a  =  a"W^^ 

Since  the  weight  of  the  motor  group  e  X  W  m  propor- 
tional to  the  power  Po, 

e  XW  =  e'  X  P2 


but 


that  is 
Then  as 
we  will  have 


i>.  =  E 


e  X  W  ^^-W 
V 

e  =  constant 
u  +  a  -[-  e  =  1 


u  =  I  -  e  -  a'WW 

and  this  formula  states  that  the  value  of  coefficient  u  di- 
minishes step  by  step  as  W  increases,  that  is,  as  the  dimen- 
sions of  the  machine  increase  step  by  step,  until  coefficient 
u  becomes  zero  for  that  value  of  W  which  satisfies  the 
equation 

I  -  e  -  a"  ^yw  =  0 
that  is 

Thus  the  useful  load  becomes  zero  and  the  airplane  would 
barely  be  capable  of  raising  its  own  dead  weight  and  the 
engine.     So  for  example  supposing 

e  =  0.25         a"  =  0.004 
we  shall  have 


Ci 


W  =  (  ~^)  =  35,000  lb. 


Now  all  the  preceding  reasoning  has  no  practical  founda- 
tion, because  it  is  based  on  a  false  premise,  that  is,  that  the 
airplanes  be  geometrically  similar.     In  fact,  it  is  not  at  all 


GREAT  LOADS  AND  LONG  FLIGHTS  211 

necessary  that  it  be  so;  on  the  contrary,  the  preceding 
reasoning  demonstrates  that  to  enlarge  an  airplane  in  geo- 
metrical ratio  would  be  an  error. 

Nature  has  solved  the  problem  of  flying  in  various  ways. 
For  example,  from  the  bee  to  the  dragon  fly,  from  the  fly 
to  the  butterfly,  from  the  sparrow  to  the  eagle,  we  find 
wing  structures  entirely  different  in  order  to  obtain  the 
maximum  strength  and  elasticity  with  the  minimum 
weight. 

It  may  be  protested  that  flying  animals  have  weights  far 
lower  than  those  of  airplanes;  but  if  we  recall,  that  along- 
side of  insects  weighing  one  ten  thousandth  of  a  pound, 
there  are  birds  weighing  15  lb.,  we  will  understand  that  if 
nature  has  been  able  to  solve  the  problem  of  flyiug  within 
such  vast  limits,  it  should  not  be  difficult  for  man,  owing  to 
his  means  of  actual  technical  knowledge,  to  create  new 
structures  and  new  dispositions  of  masses  such  as  to  make 
possible  the  construction  of  airplanes  with  dimensions  far 
greater  than  the  present  averaue  machines. 

For  example,  one  of  the  criterions  which  should  be 
followed  in  large  aeronautical  constructions  is  that  of  dis- 
tributiDg  the  masses.  The  wing  surface  of  an  airplane 
in  flight  must  be  considered  as  a  beam  subject  to  stresses 
uniformly  distributed  represented  by  the  air  reaction,  and 
to  concentrated  forces  represented  by  the  various  weights. 
Now  by  distributing  the  masses  respectively  on  the  wing 
surface,  we  obtain  the  same  effect  as  for  instance  in  a  girder 
or  bridge  when  we  increase  the  supports;  that  is,  there  will 
be  the  possibility  of  obtaining  the  same  factor  of  safety  by 
greatly  diminishing  the  dead  weight  of  the  structure. 

Another  criterion  which  will  probably  prevail  in  large 
aeronautical  constructions,  is  the  disposition  of  the  wing 
surfaces  in  tandem,  in  such  a  way  as  to  avert  the  excessive 
wing  spans. 

The  multiplane  dispositions  also  offer  another  very  vast 
field  of  research. 

As  we  see,  the  scientist  has  numerous  openings  for  the 
solution;  so  it  is  permissible  to  assume  that  with  the   in- 


212  AIRPLANE  DESIGN  AND  CONSTRUCTION 

crease  of  the  airplane  dimensions  not  only  may  it  be  possi- 
ble to  maintain  constant  the  coefficient  of  proportionality 
u  but  even  to  make  it  smaller.  Thus  with  the  increase  of 
power  we  shall  be  able  to  notably  increase  the  useful  load. 
Concluding,  we  may  say  that  the  increase  of  useful  load 
can  be  obtained  in  three  ways : 

(a)  Perfecting  the  constructive  technique  of  the  airplane 
and  of  the  engine,  that  is  reducing  the  percentage  of  dead 
weights  in  order  to  increase  u, 

(b)  Perfecting  the  aerodynamical  technique  of  the  ma- 
chine, reducing  the  percentage  of  passive  resistance  and 
increasing  the  wing  efficiency  and  the  propeller  efficiency, 

T 

so  as  to  increase  the  value  of  ratio  y  corresponding  to  the 

normal  speed  V,  and 

(c)  Finally,  increasing  the  motive  power. 

Let  us  now  pass  to  the  problem  of  increasing  the  cruising 
radius.  Let  us  call  ^S^ax.  the  maximum  distance  an 
airplane  can  cover,  and  let  us  propose  to  find  a  formula 
which  shows  the  elements  having  influence  upon  ^S^ax. 

The  total  weight  W  of  the  airplane  is  not  maintained 
constant  during  the  ffight  because  of  the  gasoline  and  oil 
consumption;  it  varies  from  its  maximum  initial  value 
Wi  to  a  final  value  Wf,  which  is  equal  to  the  difference 
between  Wi  and  the  total  quantity  of  gasoline  and  oil 
consumed. 

Let  us  consider  the  variable  weight  W  at  the  instant  t, 
and  let  us  call  dW  its  variation  in  time  dt. 

If  P  is  the  power  of  the  engine  and  c  its  specific  con- 
sumption (pounds  of  gasoline  and  oil  per  horsepower),  the 
consumption  in  time  dt  will  be 

cPdt 
and  since  that  consumption  is  exactly  equal  to  the  decrease 
of  weight  in  the  time  dt,  we  shall  have 

dW  =  -  cPdt  (1) 

From  the  formula  of  total  efficiency  we  have 

WV 
P  =  0.00267  -^^— 


GREAT  LOADS  AND  LONG  FLIGHTS  213 

then  substituting  that  value  in  (1) 

dW  =  -  0.00267cTF  -  dt 
r 

and  since 

y    ^dS 
dt 

^  =  -  0.00267c  ^ 
W  r 

and  integrating 

'cdS 


Jf=- 0.00267/^ 


The  value  of  c,  specific  consumption  of  the  engine,  can, 
with  sufficient  approximation,  be  considered  constant  for 
the  entire  duration  of  the  voyage. 

Regarding  r,  we  have  already  seen  that  it  is  a  function 
of  F;  we  shall  now  see  that  it  is  also  a  function  of  W. 
In  fact,  let  us  suppose  that  we  have  assigned  a  certain  value 
Fi  to  7;  then  the  total  efficiency  will  be 

W  W 

r  =  0.00267 7i  -^  =  const  X  y 

Supposing  now  that  W  is  made  variable;  it  would  also  vary 
P,  following  a  law  which  cannot  be  expressed  by  a  certain 
simple  mathematical  equation;  it  will  then  also  vary  ratio 

W 

-p  and  consequently  r. 

Practically,  however,  it  is  convenient,  by  regulating  the 
motive  power  and  therefore  the  speed,  to  make  value  r 
about  constant  and  equal  to  the  maximum  possible  value. 
We  can  also  consider  an  average  constant  value  for  r. 
Thus  the  preceding  integration  becomes  very  simple.  In 
fact,  as  TF  =  W^  for  5  =  0,  and  TF  =  Wf  for  S  =  S^,,_, 
we  shall  have, 

loge  Wf=-  0.00267  ^  5„,ax.  +  log.  IF. 
r 

that  is 

r  ^  ,       Wi 


214 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


and    iiitroduciiifi;    the    decimal    logariihiu    instead    of    the 
Napierian 

r  W 

>S„.,x    =  8(55  X  ^  X  log  ^  (1) 


Smax  =  865-^  '°9  F" 


C=0.45 


3600 


3200 


2S00 


2400 


^    2000 


E     1600 
IS) 


1200 


&00 


400 


1 

/ 

/ 

/ 

/ 

1 , 

^/ 

f 

/ 

/ 

/ 

/ 

/ 

/ 

// 

^  / 

f 

/ 

k 

/ 

/ 

/ 

,/ 

/  h 

¥ 

y 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

'  / 

'/ 

f 

^y 

/ 

/ 

j 

'/, 

// 

/ 

V 

K/ 

/ 

^A 

/ 

/ 

/ 

y 

/// 

// 

/ 

/ 

/ 

r> 

y 

// 

// 

/ 

/ 

y 

y/ 

/. 

/ 

y 

y' 

// 

/ 

^ 

/^ 

7A^ 

y 

^ 

V/ 

y 

y 

1.0  1.1  1,2         1.3        1.4       1.5       1,6     1.7     I.&     1.9    2.0 

Wf 
Fig.   138. 


The  cruising  radius  therefore  depends  upon  three  factors: 
1.  Upon  the  total  aerodynamical  efficiency      This  de- 
pendency is  linear;  that  is  to  say,  an  increase  of  say  10  per 


GREAT  LOADS  AND  LONG  FLIGHTS 


215 


cent,    of   aerodynamical   efficiency,    equally  increases   the 
maximum  distance  which  can  be  covered  by  10  per  cent. 

2.  Upon  the  specific  consumption  of  the  engine.     That 
dependency  is  inverse;  thus,    for  example,  if  for  we  could 


seoo 


3200 


2600 


2400 


^    2000 


1600 


1200 


.&00 


AOO 


Smax  =  865- 


log 


Wf 


0=0.54 


/ 

/ 

/ 

' 

// 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

// 

V 

/ 

/ 

y 

^ 

f 

/ 

\/ 

y 

/ 

// 

y 

A 

/I 

1 

// 

/ 

/ 

y 

/ 

, 

/ 

/ 

/ 

< 

/ 

f  / 

V 

A 

r 

/ 

,/ 

/ 

y. 

// 

/ 

/ 

^ 

'^Z 

/ 

/ 

y 

/' 

, 
'/// 

/  / 

/ 

/ 

/ 

^ 

^' 

Y/ 

y 

/ 

y^ 

^ 

//// 

V/ 

''/ 

/' 

W/. 

// 

x 

^ 

^ 

v/^ 

'^ 

y^ 

^ 

r.o 


1.2        1.3       1.4       1.5      1.&     1.7     1.8    1.9    2.0 
Wf 


reduce  the  specific  consumption  to  half,  the  radius  of  action 
would  be  doubled. 

3.  Upon  the  ratio  between  the  total  weight  of  the  airplane 
and  this  weight  diminished  by  the  quantity  of  gasohne  and 


216 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


oil  the  airplane  can  carry.  That  ratio  depends  essentially 
upon  the  construction  of  the  airplane;  that  is,  upon  the 
ratio  between  the  dead  weights  and  the  useful  load. 


Smax-=    865 -§- log    -^ 


C=0.60 


3600 


.1  1.2         1.3       1.4       15      1.6      1.7     l.a     1.9   2.0 

Fm.   140. 


We  see,  consequently,  that  the  essential  difference  between 
the  formula  of  the  useful  load  and  that  of  the  cruising  radius 
is  in  the  fact  that  in  the  latter  the  total  specific  con- 
sumption of    the  engine,  an  element  which  did  not  even 


ORE  AT  LOADS  AND  LONG  FLIGHTS  217 

appear  in  the  other  formula,  intervenes  and  has  a  great 
importance.  From  that  point  of  view,  almost  all  modern 
aviation  engines  leave  much  to  be  desired;  their  low  weight 
per  horsepower  (2  lb.  per  H.P.  and  even  less),  is  obtained  at 
a  loss  of  efficiency;  in  fact  they  are  enormously  strained  in 
their  functioning  and  consequently  their  thermal  efficiency 
is  lowered. 

The  total  consumption  per  horsepower  in  gasoline  and 
oil,  for  modern  engines  is  about  0.56  to  0.60  per  H.P.  hour; 
while  gasoline  engines  have  been  constructed  (for  dirigibles) , 
which  only  consume  0.47  lb.  per  H.P.  hour. 

A  decrease  from  0.60  to  0.48  would  lead,  by  what  we  have 
seen  above,  to  an  increase  in  the  cruising  radius  of  25 
per  cent. 

Starting  from  formula  (1)  we  have  constructed  the  dia- 
grams of  Figs.  138,  139  and  140  which  give  the  values  of 

Wi 
^m&x.  as  a  function  of  ^  for  the  different  values  of  r  and  c. 

In  Fig.  138  it  has  been  supposed  that  c  ^  0.48  lb.  per  H.P. 

hour,  in  Fig.  139  c  =  0.54  and  in  Fig.  140  c  =  0.60.     The 

diagrams  have  a  normal   scale  on   the   ordinates   and    a 

logarithmic  scale  on  the  abscissae. 

The  use  of  the  diagrams  is  most  simple,  and  permits 

rapidly  of  finding  the  cruising  radius  of  an  airplane  when 

Wi 
r,  c  and  ~,  are  known. 
W  f 

Before  closing  this  chapter,  it  is  interesting  to  examine 
as  table  resuming  the  characteristics  of  the  best  types  of 
military  airplanes  adopted  in  the  recent  war,  for  scouting, 
reconnaissance,  day  bombardment,  and  for  night  bombard- 
ment. 

In  Table  6  the  following  elements  are  found: 
Wi  =  weight  of  the  airplane  with  full  load. 
Wf  =  weight  of  the  empty  machine  with  crew  and 
instruments  necessary  for  navigation. 

W  ■ 

^  =  ratio  between  initial  weight   and  final  weight. 

W  f 

We  shall  suppose  therefore  that  all  the  useful  load,  com- 
prising military  loads,  consists  of  gasoline  and  oil. 


218  AIRPLANE  DESK.'N  AND  CONSTRUCTION 

P  =  iiuixiinuin  i)o\vor  of  the  engine. 

Wi 

-p-  =  weight  per  horsepower. 

Wi 

—7^  =  load  per  unit  of  the  wing  surface. 

^max.  =  the  maximum  horizontal  speed  of  the  airplane. 

^max.  =  the  maximum  ascending  speed  averaged  from 

ground  level  to  10,000  ft. 

W   X  V        . 

P'  =  — — "^-"  is  the  power  absorbed  in  horsepower 

0.75  X  550  ^ 

to  obtain  the  ascending  speed  v^^^^,  supposing  a  propeller 

efficiency  equal  to  0.75. 

\p p/ 

V  =  7jnax.-\/— p —  is   the    horizontal    speed    of    the 

airplane  for  which  we  have  the  maximum  ascending  speed 

'  max.* 

r  -  0.00267^^'  ^^""^-^  is    the    total    efficiency    cor- 
responding to  7„ax.- 

Wi  XV    . 
r'  =  0.00267  ~ py-    is    the    total    efficiency    corre- 
sponding to    v. 

S  and  S'  =  the  maximum  distances  covered  in  miles 

Wi  Wi 

corresponding  to  F^ax.  f,  tj^*  and    V,    r',  ^  respectively, 

supposing  c  =  0.60. 

Of 

„    =  the  gain  in  distance  covered,  flying  at  speed  V 

instead  of  V. 

0  85  P 
W'i  =  375  X  r'  X  ™y7-    is  the  total  weight  the  air- 
plane   can    lift    at    speed   V,  supposing    an  allowance  of 
excess  power  of  15  per  cent. 

W'f  =  Wf  +  H  {W'i  -  Wi)  is  the  new  value  of  the 
final  weight,  supposing  that  >^  of  the  gain  in  weight  is 
necessary  to  reinforce  the  airplane  so  as  to  have  the  same 
factor  of  safety. 

W'i 

=1^,-  =  the  new  ratio  between  the  new  initial  weight 


GREAT  LOADS  AND  LONG  FLIGHTS 


219 


^ 

C-l 

1 

cc!^ 

C<1            --1 

r-i 

—1 

-S 

^'s 

g        S 

cj 

00 

lO           t^ 

to 

gK^l^-ii 

O            CO 

^ 

^ 

•-I 

. 

^    § 

§ 

hl^aK^ii 

rt             00 

00 

00 

•'•'Is-, 

s   ^ 

g 

in 

fe:|^ 

w" 

m 

^5 

5    g§ 

?5 

i 

o       o 

fe:a 

s    § 

^ 

00        to 

o 

^^1^ 

"^ 

.-<                l-H 

^ 

1-1 

m 

«      o 

^■s 

"    "^ 

.  ® 

CO         o 

5^ 

s 

-1 

(N           ■* 

ffli 

g   5 

^ 

s 

M           •* 

cc 

M 

o 

M        n 

m 

IM 

fl 

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2      S 

S 

S 

r^ 

s 

^ft,^ 

■Das  J3d  -^j 
•xBtaa 

S      ^ 

o 

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M^' 

Is. 

(N           IN 

00 

Sh5S.^4i 

00           t- 

t- 

00 

<o        b 

■      o 

Ol 

SK^al 

l^           Zl 

o 

o 

«-^ 

m        o 

^ 

§ 

^^ 

'I'        'f 

CV 

m 

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1        1 

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§        § 

§ 

5=^ 

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N           C? 

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2 

a 

2  § 

>> 

OS 

5 

C3 

!0      ^ 

Q 

S      ^ 

0) 

fe 

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SI  1 

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1 

lit 

H 

H 

H-^ 

220  AIRI'LAXE  DESIGN  AND  CONSTRUCTION 

and  the  new  final  weight. 

— J-'  =  the  new  load  per  unit  of  wing  surface. 

-p-^  =  the  new  load  per  horsepower. 

S"  =  the  maximum  distance  covered  corresponding  to 

:^  and  to  r  . 

The  examination  of  Table  7  enables  making  the  following 
deductions: 

1.  Whatever  be  the  type  of  machine  it  is  convenient  to 
fly  at  a  reduced  speed  T"',  because  in  that  way  the  cruising 
radius  increases. 

2.  All  war  airplanes  are  utiUzed  very  little  as  to  useful 
load  and  consequently  as  to  cruising  radius.     As  column 

o// 

^,    shows,  they  could  have  a  radius  of  action  far  superior 

if  their  enormous  excess  of  power  could  be  renounced.  The 
gain  is  naturally  stronger  for  the  more  light,  quick  air- 
planes, as  for  instance  the  scout  machines,  than  for  the 
heavier  types. 


PART  IV 
DESIGN  OF  THE  AIRPLANE 


CHAPTER  XVI 
MATERIALS 

The  materials  used  in  the  construction  of  an  airplane  are 
most  varied.  The  more  or  less  suitable  quality  of  material 
for  aviation  can  be  estimated  by  the  knowledge  of  three 
elements:  specific  weight,  ultimate  strength  and  modulus 
of  elasticity. 

Knowing  these  elements  it  is  possible  to  calculate  the 
coefficients 

_  ultimate  strength  in  pounds  per  square  inch 
^  ~"      specific  weight  in  pounds  per  cubic  inch 
and 

modulus  of  elasticity  in  pounds  per  square  inch 
specific  weight  in  pounds  per  cubic  inch 


A, 


The  coefficients  Ai  and  A  2  are  not  plain  numbers,  but  have 
a  Unear  dimension,  and  a  very  simple  physical  inter- 
pretation can  be  given  to  them;  that  is.  Ax  measures  the 
length  in  inches  which,  for  instance,  a  wire  of  constant 
section  of  a  certain  material  should  have  in  order  to  break 
under  the  action  of  its  own  weight;  A 2  instead,  measures 
the  length  in  inches  which  a  wire  (also  of  constant  section) 
of  the  material  should  have  in  order  that  its  weight  be 
capable  of  producing  an  elongation  of  100  per  cent. 

The  higher  the  coefficients  Ai  and  A 2,  the  more  suitable 
is  a  material  for  aviation. 

It  may  be  that  two  materials  have  equal  coefficients  A 1 
and  A 2,  but  different  specific  weights.     In  that  case  the 

221 


222 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


material  of  lower  specific  weight  is  preferable  when  there 
are  no  restrictions  as  to  space;  instead,  preference  will  be 
given  to  the  material  of  higher  specific  weight  when  space 
is  limited.  This  because  of  structural  reasons,  or  in  order 
to  decrease  head  resistance. 

In  all  of  the  following  tables  whenever  possible,  we  shall 
give  the  values  of  specific  weight  and  coefficients  Ai  and 
A,. 

We  shall  briefly  review  the  principal  materials,  grouping 
them  into  the  following  broad  categories: 

A.  Iron,  steel  and  their  manufactured  products. 

B.  Various  metals. 

C.  Wood  and  veneers. 

D.  Various  materials  (fabrics,  rubbers,  glues,  varnishes, 
etc.). 

A.     IRON,  STEEL  AND  THEIR   COMMON   FORM  AS   USED   IN 
AVIATION 

Iron  and  steel  are  employed  in  various  forms  and  for 
various  uses;  for  forged  or  stamped  pieces,  in  rolled  form 
for  bolts,  in  sheets  for  fittings,  plates,  joints,  in  tinned  or 
leaded  sheets  for  tanks,  etc. 


Fio.  141. 


In  Table  7  are  shown  the  best  characteristics  required 
•of  a  given  steel  according  to  the  use  for  which  it  is 
intended. 

Steel  wires  and  cables  are  of  enormous  use  in  the  con- 
struction of  the  airplane.  Tables  8  and  9  give  respectively 
tables  of  standardized  wires  and  cables. 


MATERIALS 


223 


o  c 
OS 


%1    22 


o  o 

O     O 

R8 

RS   : 

II 

U   : 

CO     r-t 

CO    -4 

■o  o 

t^    OS 

o  d 


o  o 


n 

o_o_ 

o  o 

lO    1-0 


sggs 

o  o  o  o 


lis 


U5   lO 

o  o 
d  d 


siii 


o  o 
o  o 
d  d 


lO  iO  lO  o 

•O  lO  lO  o 

O  O  .-H  <M 

d  d  o  d 


c  o.S  a  o 


B 


-<    -H    (N    (N    IM    (N 


§§ 


ass'.s 


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AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table  8.- 


-SizEs,  Wekjhts  and  Physical  Properties  of  Steel  Wire 
English  Units 


Diameter.!     l^^% 
ft.-lb. 


Torsion 
test* 


Bend 

test 


Breaking 
strength 


Tensile 
strength 


Number 

of  turns 

(minimum) 


Number 

of  bends 

(minimum) 


Pounds 
(minimum) 


Lb.  per 

sq.  in. 

(minimum) 


6 

0.162 

7.010 

16 

5 

4500 

219,000 

7 

0.144 

5.560 

19 

6 

3700 

229,000 

8 

0.129 

4.400 

21 

8 

3000 

233,000 

9 

0.114 

3.500 

23 

9 

2500 

244,000 

10 

0.102 

2.770 

26 

11 

2000 

245,000 

11 

0.091 

2.200 

30 

14 

1620 

249,000 

12 

0.081 

1.744 

33 

17 

1300 

252,000 

13 

0.072 

1.383 

37 

21 

1040 

255,000 

14 

0.064 

1.097 

42 

25 

830 

258,000 

15 

0.057 

0  870 

47 

29 

660 

259,000 

16 

0.051 

0.690 

53 

34 

540 

264,000 

17 

0.045 

0.547 

60 

42 

425 

267,000 

18 

0.040 

0.434 

67 

52 

340 

270,000 

19 

0.036 

0.344 

75 

70 

280 

275,000 

20 

0.032 

0.273 

84 

85 

225 

280,000 

21 

0.028 

0.216 

96 

105 

175 

284,000 

Metric  Units 


American 

Diameter, 

Weight 
per  100 
m.,  kg. 

Torsion 

test* 

Bend 

test 

Breaking 
strength 

Tensile 
strength 

wire 
gage 

Number 

of  turns 

(minimum) 

Number 

of  bends 

(minimum) 

Kilograms 
(minimum) 

Kg.  per 

sq.  mm. 

(minimum) 

6 

4.115 

10.440 

16 

5 

2041.0 

154.0 

7 

3.665 

8.280 

19 

6 

1678.0 

161.1 

8 

3.264 

6.550 

21 

8 

1361.0 

163.8 

9 

2.906 

5.210 

23 

9 

1134.0 

171.6 

10 

2.588 

4.120 

26 

11 

907.0 

172.2 

11 

2.305 

3.280 

30 

14 

735.0 

175.0 

12 

2.053 

2.597 

33 

17 

590.0 

177.2 

13 

1.828 

2.060 

37 

21 

472.0 

179.4 

14 

1.628 

1.635 

42 

25 

376.5 

181.5 

15 

1.450 

1.295 

47 

29 

299.4 

182.1 

16 

1.291 

1.028 

53 

34 

244.9 

185.6 

17 

1.150 

0.814 

60 

42 

192.8 

187.7 

18 

1.024 

0.646 

67 

52 

154.2 

189.8 

19 

0.912 

0.512 

75 

70 

127.0 

193.4 

20 

0.813 

0.406 

84 

85 

102.1 

196.8 

21 

0.724 

0.322 

96 

105 

79.4 

199.6 

'The  minimum  number  of  complete  turns  which  a  wire  must  withstand 
may  be  computed  from  the  formula: 

2.7  _   68^6 

diameter  in  inches        dia.  in  millimeters 


MATERIALS  225 

T.^BLE  9. — Weights,   Sizes  and  Strength   of  7  X  19   Flexible   Cable 


English  units 

Metric  units 

Diameter,  in. 

Approxi- 
mate 
weight,  lb. 
per  100  ft. 

Breaking 

strength, 

lb. 

(minimum) 

Diameter, 
mm. 

Approxi- 
mate 
weight,  kg. 
per  100  m. 

Breaking 

strength 

kg. 

(nainimum) 

0.375  (%; 

26.45 

14,400 

9.525 

39.36 

6,532 

0.344  (IK2) 

22.53 

12,500 

8.731 

33.53 

5,670 

0.312  (Ke) 

17.71 

9,800 

7.938 

26,35 

4,445 

0.281  ir32) 

14.56 

8,000 

7.144 

21.67 

3,629 

0.250  (K) 

12.00 

7,000 

6.350 

17.86 

3,175 

0.218  (%2) 

9.50 

5,600 

5.556 

14.14 

2,540 

0.187(^6) 

6.47 

4,200 

4.763 

9.63 

1,905 

0.156  (M2) 

4.44 

2,800 

3.969 

6.61 

1,270 

0.125  (Vs) 

2.88 

2,000 

3.175 

4.29 

907 

The  formation  of  cables  is  shown  in  Fig.  141.  The  cable 
is  made  of  7  strands  of  19  wires  each;  the  figure  shows  how 
these  strands  are  formed.  The  smaller  diameters  are  extra- 
flexible  so  that  they  can  be  used  as  control  wires  as  they 
well  adapt  themselves  in  pulleys. 

Recently,  steel  streamline  wires  have  been  introduced  to 
replace  cables,  in  order  to  obtain  a  better  air  penetration. 
Fig.  142  shows  the  section  of  one  nf  su^h  wires.     Their  use 


Fig.   142. 

has  not  yet  greatly  broadened,  especially  because  their 
manufacture  has  until  now  not  become  generalized.  It 
is  foreseen  though,  that  the  system  will  rapidly  become 
popular. 

We  shall  now  take  up  the  attachments  of  wires  and 
cables.  The  attachment  most  commonly  used  for  wu-es, 
is  the  so-called  "eye"  (Fig.  143).  It  is  an  easy  attachment 
to  make,  but  it  reduces,  however,  the  total  resistance  of 
the  wire  by  20  to  30  per  cent,  depending  on  the  diameter  of 
the  wire. 


226 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Wires  with  larger  threaded  ends  (called  ''tie  rods") 
(Fig.  144),  are  becoming  of  general  use.  A  very  good 
attachment  can  be  obtained  by  covering  the  bent  wire 
with  brass  wire  and  soldering  the  whole  with  tin  (Fig. 
145);  in  this  way  an  attachment  is  obtained  which  gives 


Fi.;.    H;J 


Fig.  144. 


Fig.   145. 


Fig.   146. 


100  per  cent,  of  the  wire  resistance.     The  soldering  is  made 
with  tin  in  order  to  avoid  the  annealing  of  the  wire. 

The  best  attachment  of  cables  is  made  by  so-called 
spUcing  after  bending  it  around  a  thimble  (Fig.  146),  which 
is  made  either  of  stamped  sheets  or  of  aluminum  (Fig.  147). 


MATERIALS 


227 


Steel  is  also  much  used  in  tube  form,  either  seamless, 
cold  rolled,  or  welded.  Table  10  gives  the  characteristics 
of  the  steel  of  various  tube  types. 


^ 

4M 


Fig.  148. 


Tables  11  and  12  give  the  standard  measurements  of 
round  tubes  with  the  values  of  weight  in  pounds  per  foot 
and  the  values  of  the  polar  moment  of  inertia  in  in.^ 


228 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Steel  tubing  having  a  special  profile  formed  so  as  to  give 
a  minimum  head  resistance  is  also  greatly  used  for  inter- 
plane  struts  as  well  as  for  all  other  parts  which  must 
necessarily  be  exposed  to  the  relative  wind. 

The  best  profile  (that  is,  the  profile  which  unites  the 
best  requisites  of  mechanical  resistance,  lightness  and  air 
penetration)  is  given  in  Fig.  148  which  also  shows  how  it 
is  drawn,  and  gives  the  formulae  for  obtaining  the  peri- 
meter, the  area,  and  the  moments  of  inertia  I:,  and  /„ 
about  the  two  principal  axes  as  function  of  the  smaller 
diameter  d  and  thickness  t. 


Tables  13  and  14  give  all  the  above  mentioned  values, 
and  furthermore  the  weight  per  linear  foot  for  the  more 
commonly  used  dimensions. 

A  greatly  used  fitting  in  aeronautical  construction  is  the 
turnhuckle,  which  is  designed  to  give  the  necessary  tension 
to  strengthening  or  stiffening  wires  and  cables. 

A  turnbuckle  is  made  of  a  central  barrel  into  which  two 
shanks  are  screwed  with  inverse  thread;  the  shanks  have 
either  eye  or  fork  ends*  thus  we  have  three  classes  of 
turnbuckles : 

Double  eye  end  turnbuckle  (Fig.  149a) 

Eye  and  fork  end  turnbuckle  (Fig.  1496) 

Double  fork  end  turnbuckle  (Fig.  149c) 


MATERIALS 


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^    ^    ^    C^    <N    CS 

i 

1 

3^ 

1.272 
1.675 
2.150 
2.425 
2.750 
3.222 

ic  0  0  0  0  0 

CO    -^    ■*    >— 1    <35   t^ 

01  10  00  CO  t^  0 

<-<    (N    (N    CO    CO    Tji 

CO    -*    CD   0    (N   00 
00    (N   t^    CO   CO    CO 

CJ    CO   CO    ■«*    -"^^    "5 

I' 

S52§§?S 

g?2?5§S§ 

<N  00  uo  CO  00  0 

'-'    (N    CO   CO   ■*    ■* 

(N   CO   '^   "*   10   CO 

^    -*    10   CO   CO   00 

A 

CO    ■<*    CO    t^    !>    05 

10  r^  00  0  ^  ^ 

<N    10    (N    t-    0    00 

CO    Tf    05    Tj<    rt*    CD 
00    05    0    IM    CO    lO 

000000 

0     0     0     0     ^     rH 

0     0     r-H     ^     ,-(     rt 

E 

000000 

000000 

000000 

(N    CO    -^    r}<    UJ    CO 

00  0  (N  0  0  0 

CO   Iv   CO    C^    ^    CO 
CO   ■*   «0   CD   I>   t^ 

iiliis 

_2 

(M    C<)    <N    (N    (N    (N 

00   00   00   00    00   00 

000000 

(N    iM    (N    IM    (N    (N 

•^    ■*•<*■*    ""^i    ■<*< 

05    0>    05    05    05    05 

000000 

CO   CO   CO    CD    CO   CO 

00   00   06   00   00   06 
05    05    05    C5    05    05 

1>  t^  t^  l>  1>  I> 

s  s  ^  s  s  § 

05    05    05    Cft    05    OJ 

s  s  ^  s  s  s 

^    ^    ^    S    S    ^ 

a 

a 

05    10   CO   -*    05   »c 

0  0  0  §  ^  d 

065 
083 
094 
109 
125 
134 

||§§gg 

000000 

0  0  0  0  c  0 

000000 

B 
B 

ic  0  0  ic  0  0 

■*     10    'H     00    t^    t^ 

0  0  10 

0   lO 

.-<   ^    (N   (N   (M   CO 

--1    C^    (N    IM    CO   CO 

C<J    (N    (N   CO    CO    CO 

D  =  90  mm. 

=  3.54  in. 
d  =  30  mm. 

=  1.18  in. 

D   =  105  mm. 

=  3.94  in. 
d  =  35  mm. 

=  1..38in. 

D   =  120  mm. 

=  4.72  in. 
d  =  40  mm. 

=  1.57  in 

234  AIRPLANE  DESIGN  AND  CONSTRUCTION 

For  tuiiiljiiekles  as  well  as  for  bolts,  the  reader  may  easily 
})rocure  from  the  respective  firms,  tables  of  standard 
measurements  with  indications  of  breaking  strength. 

B.     VARIOUS  METALS 

Table  15  gives  the  physical  and  chemical  characteristics 
of  various  metals  most  commonly  used;  that  is,  copper, 
brass,  bronze,  aluminum,  duraluminum,  etc. 

Copper  and  brass  are  generally  used  for  tanks,  radiators, 
and  the  relative  piping  systems. 

Aluminum  is  used  rather  exclusively  to  make  the  cowling 
which  serves  to  cover  the  motor.  Aluminum  can  also  be 
used  for  the  tanks. 

High  resistance  bronzes  are  used  for  the  barrels  of  turn- 
buckles. 

Tempered  aluminum  alloys,  have  not  become  of  general 
use  at  all,  because  their  tempering  is  very  delicate  and  it  is 
easily  lost  if  for  any  reason  the  piece  is  heated  above  400°r. 

We  call  especial  attention  to  the  un tempered  aluminum 
alloy  which,  not  requiring  any  treatment,  has  a  resistance 
and  an  elongation  comparable  to  those  of  homogeneous 
iron,  although  its  specific  weight  is  %  that  of  iron. 

C.     WOODS 

Wood  is  extensively  used  in  the  construction  of  the 
airplane;  either  in  soUd  form  or  in  the  form  of  veneer. 

Tables  16  and  17  give  the  characteristics  of  the  principal 
species  of  woods  used  in  aviation.  ^ 

Cherry,  mahogany,  and  walnut  are  used  especially  for 
manufacturing  propellers.  For  the  wing  structure,  yellow 
poplar,  douglas  fir,  and  spruce  are  especially  used. 

Yellow  birch,  yellow  poplar,  red  gum,  red  wood,  mahog- 
any (true),  African  mahogany,  sugar  maple,  silver  maple, 
spruce,  etc.,  are  especially  used  in  manufacturing  veneers. 

Great  attention  must  be  exercised  in  the  selection  of  the 

'  This  table  has  been  compiled  by  the  Forest  Products  Laboratory.  U.  S. 
Forest  Service.     Madison,  Wisconsin. 


MATERIALS 


235 


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236 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table  16. — Properties  o 
Strength  Values  at  15  Per  Cent.  Mo 


Specific  gravity 

based  on 

volume  and 

weight  when 

oven  dry 

Specific 

weight 

at  15 

per  cent. 

moisture 

Static 

Common  and  botanical  names 

Fiber 
stress 

at 
elastic 
limit 

Modulus 

of 
rupture 

Aver- 
age 

Mini- 
mum 
per- 
mitted 

Lb.  per 
cu.  ft. 

Lb.  per 

sq.  in. 

Lb.  per 
sq.  in. 

(/6) 

Ash  (commercial  white)    (Fraxinus  Ameri- 
cana; Fraxinus  LanceoLata;  Fraxinus  Quad- 

0.62 
0.5,3 
0.40 
0.66 
0.67 
0.53 
0.43 
0.66 
0.53 

0.81 
0.54 
0.50 
0.66 

0.72 
0.42 
0.56 

0.56 
0.48 
0.36 
0.60 
0.61 
0.48 
0.39 
0.60 
0.48 

0.73 
0.50 
0.46 
0.60 

0.65 
0.38 
0.52 

40 
35 
25 
41 
43 
35 
28 
44 
34 

50 
36 
34 

42 

46 
28 
38 

7700 
5800 
4700 
7400 
8400 
7300 
4500 
6700 
6700 

8900 
7000 
7100 
8100 

6700 
4800 
7900 

12700 
10500 

7200 
12600 
13500 
10600 

7000 
12500 
10400 

16300 
10000 
10400 
12900 

12000 
7500 
11900 

Ash  (black)  (Fraxinus  Nigra) 

Bass  wood  {Tillia  Americana)   

Birch  (Betula  Lutea,  Lenta) 

Cherry  (black)  (Prunus  Serotina) 

Gum  (red)  {Liquidnmhar  Styraciflua) 

Hickory    (true    hickories)    {Higoria  Glabra, 

Mahogany  (true)   (Swietenia  Mahagoni) 

Mahogany  (African)   (Khayn  Senegalensis) . 

Oak  (commercial  white)  (Quercus  Alba  Mac- 

Poplar  (yellow)  '(Liriodendriim  Tulipifera) . . 

timbers  for  aviation  uses;  they  must  be  free  from  disease, 
homogeneous,  without  knots  and  burly  grain,  and  above  all 
they  must  be  thoroughly  dry.  Artificial  seasoning  does  not 
decrease  the  physical  qualities  of  wood,  but,  on  the  con- 
trary, it  improves  them  if  such  seasoning  is  conducted  at  a 
temperature  not  above  100°r.  and  is  done  with  proper 
precautions. 

It  is  very  important,  especially  for  the  long  pieces,  as  for 
instance  the  beams,  that  the  fiber  be  parallel  to  the  axis  of 
the  piece,  otherwise  the  resistance  is  decreased. 

Furthermore,  it  is  important  to  select  by  numerous 
laboratory  tests  the  quality  of  the  wood  to  be  used,  because 
between  one  stock  of  wood  and  another,  great  differences 
may  usually  be  found. 

As  an  example  of  the  importance  which  the  value  of  the 
density  of  wood  has  upon  the  major  or  minor  convenience  of 
its  use  in  the  manufacture  of  a  certain  part,  let  us  suppose 
that  we  design  the  section  of  a  wing  beam  which  has  to 


MATERIALS 


237 


p  Various  Hard  Woods 
isture,  for  Use  in  Airplane  Design 


bending 

Compress- 
ion parallel 
to  grain 
max. 
crushing 
strength 

Compress- 
ion perpen- 
dicular to 
grain  fiber 
stress  at 
elastic 
limit 

Shearing 
strength 
parallel 
to  grain 

Hardness 
side  load 
required 
to  imbed 
0.444  in. 
ball  to 
one-half 

its 
diameter 

/6 

/6 

fb 

Modulus 

of 
elasticity 

Work 

to 
maxi- 
mum 
load 

E 

S.W. 

S.W. 

1000  lb. 

In.    lb. 

Lb.  per 

Lb.  per 

Lb.  per 

persq. 

per  cu. 

sq.  in. 

sq.  in. 

sq.  in. 

Lb. 

in.  (E) 

'- 

(/c) 

(/O 

1500 

14.2 

6000 

1300 

1750 

1150 

0.472  0.138 

317.5 

37500 

1400 

14.1 

4900 

800 

1350 

740 

0.467|0. 1281300. 0  40000 

1300 

6.4 

38C0 

400 

880 

340 

0.503|0.122'288. 0  52000 

1500 

13.3 

5900 

1100 

1700 

1060 

0.468  0.135  307.4  36585 

1800 

17.6 

6600 

1060 

1620 

1070 

0.489  0.120  314   0  41860 

1400 

12.0 

5800 

700 

1500 

830         0.548  0.141302.8  40000 

1200 

7.3 

3800 

400 

800 

380 

0.527  0.114  250.0  42855 

1400 

19.3 

5800 

1200 

1650 

1200 

0.464  0.132  284.1  31818 

1400 

11.0 

4900 

700 

1500 

650 

0.471  0.144  305.9  41777 

J             1 

1900 

28.0 

7300 

1800 

1800 

0.448  0.110  326.0  38000 

1300 

9.1 

5500 

1000 

1420 

"860         0.5500.1421277.8  36111 

1400 

10.3 

5100 

900 

1270 

730 

0.489,0.102  305.9  41777 

1600 

12.9 

6500 

1200 

1990 

1200 

0.504  0.155  307.1  38095 

1400 

12.7 

5900 

1300 

1760 

1270 

0.490  0.147  260.9  30435 

1300 

6.2 

4100 

400 

900 

370 

0.546  0.120  267.9  46430 

1500 

13.1 

6100 

1000 

1300 

950 

0.513  0.110  313.2  39474 

resist,  for  example,  to  a  bending  moment  of  20,000  Ib.-inch; 
and  let  us  suppose  that  the  maximum  space  which  it 
is  possible  to  occupy  with  this  section  is  that  of  a 
rectangle  having  a  base  equal  to  2.2"  and  a  height  equal  to 
2.8".  We  shall  make  a  comparison  between  the  use  of 
spruce  and  the  use  of  douglas  fir,  for  which  the  value  of 
coefficient  Ai  is  about  the  same.  Table  17  gives  a  modu- 
lus of  rupture  of  7900  lb.  per  sq.  in.  for  the  spruce  with  a 
weight  per  cu.  ft.  of  27  lb.;  that  is,  0.0156  lb.  per  cu.  inch. 
Since  the  maximum  bending  moment  is  equal  to  20,000  Ib.- 
inch,  the  section  modulus  of  the  section  will  equal 
„.        20,000       ^  Ko  •     u^ 

^^^  =  -7-;9oo  =  '-^^  ^"^^ 

For  fir,  instead,  we  shall  have 


W,  = 


20,000 


9,700 
with  a  density  of  0.0197  lb.  cu.  in 


=  2.06  in.--" 


238 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table   17.— Properties 
Strength  Values  at  15  Per  Cent.  M 

Specific  gravity 

based  on 

volume  and 

weight  when 

oven  dry 

Specific 

weight 

at  15 

per  cent. 

moisture 

Static 

Common  and  botanical  names 

Fiber 

stress 

at 
elastic 
limit 

1 

Modulus 

of 
rupture 

Mini- 
Aver-       mum 
age          per- 
mitted 

Lb.  per 

cu.  ft. 

Lb.  per 

sq.  in. 

Lb.  per 

Cedar  (incense)  {Libocedrua  Decurrens) 

Cedar  (Port  Orford)   (Chamaecyparis  Law- 

soniana) 

Cedar  (western  red)  (Thuja  Plicata) 

Cedar  (white  northern)  {Thuja  Occidentalis) 
Fir  (Douglas)                                          

0.36 

0.47 
0.34 
0.32 
0.52 
0.39 
0.45 
0.39 

0.41 
0.47 

0.32 

0.42 
0.31 
0.29 
0.47 
0.36 
0.40 
0.36 

o;42 

26 

31 
23 

22 
34 
27 
29 
27 

27 
31 

4900 

6200 
4200 
4200 
0800 
5300 
5100 
5100 

5100 
5100 

7100 

10300 
6400 
5800 
9700 
7400 
7800 
7400 

7900 
8800 

Pine  (western  white)  {Pinus  Monticola) 

Pine  (white)  (Pinus  fitrobiis)                      .... 

Spruce   (red,   white,   Sitka)    (Picea  Rubens; 

Canaden^i.t  Sitrhevxix) 

Cypress  (bald)  (T-ixodium  Distirhitm) 

Let  us  call  x  the  thickness  of   the    flange   (Fig.   150a). 
Making  the  thickness  of  the  web  equal  to  0.8x,  the  section 
modulus  and  the  area  of  the  section  will  be  respectively 
W  =  H  [2.2"  X  2.8''2  -  (2.2  -  0.8a;)(3  -  2xy]  cu.  in. 
A  =  2.2''  X  2.8  -  (2.2  -  0.8a:)  X  (3  -  2x)  sq.  in. 
For  spruce 


W  =  W 


2.53  in.= 


from  which  we  have 


X  =  0.9" 
A  =  4.37  sq. 

For  fir  we  shall  have  analogously 

X  =  0.65" 
A  =  3.29  sq. 


in. 


Consequently,  the  spruce  beam  will  weigh  4.37  X  0.0156 
=  0.069  lb.  per  in.  of  length,  while  the  fir  beam  will  weigh 
3.29  X  0.0197  =  0.064  lb.  Supposing  then  for  instance, 
that  the  total  length  of  the  beams  be  150  ft.,  i.e.,  1800  in., 
the  weight  of  the  spruce  beams  would  be  1800  X  0.069 
=  124  lb.,  while  the  weight  of  the  fir  beams  would  be  1800  X 


MATERIALS 


239 


OF  Vahious 

Conifers 

oisture, 

or  Use  in  Airplane  Desifin 

bending 

Modulus 
of 

elasticity 

Work 

to 
maxi- 
mum 
load 

ion  parallel 
to  grain 

max. 
crushing 
strength 

Compress- 
ion perpen- 
dicular to 
grain  fiber 
stress  at 
elastic 
limit 

Shearing 
strength 
parallel 
to  grain 

Hardness 
side  load 
required 
to  imbed 
0.444  in. 
ball  to 
one-half 

its 
diameter 

S.W. 

Ai  = 

E 
S.W. 

1000  lb. 

In.    lb. 

Lb.  per 

Lb.  per 
sq.  in. 

Lb.  per 

per  sq. 

per  cu. 

sq.  in. 

sq.  in. 

Lb. 

in.  {E) 

in. 

(/O 

(A) 

1000 

6.0 

4300 

600 

850 

430 

0.606  0.120  273.1  38464 

1 

1700 

9.7 

5300 

700 

1160 

580 

0.51310. 112:332. 3  54840 

1000 

5.5 

4000 

400 

790 

300 

0.625:0.123:278.3  43478 

750 

5.1 

3400 

350 

800 

300 

0.586  0.138  263.6  34091 

1780 

7.2 

6000 

750 

1020 

580 

0.619  0.104  285.3  52353 

1100 

5.0 

4300 

540 

950 

410 

0,58110.128  274.1  40740 

1400 

6.9 

4800 

480 

670 

360 

0.615  0.086  269.0  48276 

1200 

6.1 

4500 

530 

850 

380 

0.608  0.115  274.1  44444 

1            1 

1300 

7.4 

4300 

500 

920 

430 

0.5440.117292.648148 

1300 

6.8 

5400 

670 

940 

460 

0.012  0.107,284.0  41936 

0.064  =  115  lb.;  that  is,  a  gain  of  9  lb.,  more  than  7  per 
cent.,  would  be  obtained. 

If  we  use  elm,  which  has  the  same  coefficient  A  i  as  the 
preceding  woods,  but  a  resistance  of  12,500  lb.  per  sq.  in. 
and  a  weight  per  cu.  in.  of  0.0255  lb.  we  would  have 
(Fig.  1596) 

X  =  0.48" 

A  =  2.44  sq.  in. 

with  a  weight  per  inch  of  2.44  X  0.0255  =  0.062  and  for 
1800  in.,  a  weight  of  112  lb.;  that  is,  a  gain  of  about  10  per 
cent,  over  the  spruce. 

Let  us  now  examine  an  inverse  case,  a  case  in  which  the 
piece  is  loaded  only  to  compression  and  no  limit  fixed  upon 
the  space  allowed  its  section;  this  for  instance  is  the  case  of 
fuselage  longerons.  Then  the  product  E  X  I  (elastic  mod- 
ulus X  moment  of  inertia) ,  is  of  interest  for  the  resistance 
of  the  piece. 

Let  us  suppose  that  the  longeron  has  a  square  section  of 
side  X.     We  then  have 

1     . 


/  = 


12 


240 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Supposing  that  we  have  two  kinds  of  wood  of  modulus 
El  and  Eo  and  specific  weight  Wi  and  Wo  respectively;  and 
suppose  that  coefficient  A2  be  the  same  for  both  kinds, 
that  is 


DOUGLAS   FIR 


ELM 


Fig.   150. 

Let  US  call  /i  and  1 2  the  moments  of  inertia  which  the 
section  must  have  respectively,  according  as  to  whether  it  is 
made  of  one  or  the  other  quality  of  wood.     If  we  wish  the 
piece  to  have  the  same  resistance  in  both  cases  then 
Eili  =  E2I2 


MATERIALS  241 

that   is 

from   which 

W,  xi'  =  W2  X2'  (1) 

The  weights  per  Hnear  inch  evidently  will  be  in  both  cases 

TFi  X  xi^  and  W2  X  X2' 
and  their  ratio  w  will  be 

Wi  X  xi^ 


w  = 


But  from  (1) 
consequently 


W2  X  x^ 

TTi  X  X,'-  ^  xl 
Wi  X  X22       xi^ 


that  is,  the  piece  having  the  greater  section  will  weigh  less, 
therefore  it  is  convenient  to  use  the  material  of  smaller 
specific  weight. 

Let  us  now  consider  the  veneers,  which  have  become  of 
very  great  importance  in  the  construction  of  airplanes. 

Wood  is  not,  of  course,  homogeneous  in  all  directions,  as 
for  instance,  a  metal  from  the  foundry  would  be;  its  struc- 
ture is  of  longitudinal  fibers  so  that  its  mechanical  qualities 
change  radically  according  to  whether  the  direction  of  the 
fiber  or  the  direction  perpendicular  to  the  fiber  is  considered. 
Thus,  for  instance,  the  resistance  to  tension  parallel  to  the 
fiber  can  be  as  much  as  20  times  that  perpendicular  to  the 
fiber,  and  the  elastic  modulus  can  be  from  15  to  20  times 
higher.  Yice  versa,  for  shear  stresses  we  have  the  reverse 
phenomenon;  that  is,  the  resistance  to  shearing  in  a  direc- 
tion perpendicular  to  the  fiber  is  much  greater  than  in  a 
parallel  direction  to  the  fiber.  Now  the  aim  in  using  veneer 
is  exactly  to  obtain  a  material  which  is  nearly  homogeneous 
in  two  directions,  parallel  and  perpendicular  to  the  fiber. 

Veneer  is  made  by  glueing  together  three  or  a  greater 
odd  number  of  thin  pUes  of  wood,  disposed  so  that  the  fibers 


242 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


cross  each  other  (Fig.  151).  It  is  necessary  that  the  num- 
ber of  plies  be  odd  and  that  the  external  phes  or  faces 
have  the  same  thickness  and  be  of  the  same  quality  of  wood, 
so  that  they  may  all  be  influenced  in  the  same  way  by 
humidity,  that  is,  giving  perfect  symmetrical  deformations, 
thus  avoiding  the  deformation  of  the  veneer  as  a  whole. 

It  is  advisable  to  control  the  humidity  of  the  plies  during 
the  manufacturing  process,  so  that  the  finished  panels  may 
have  from  10  to  15  per  cent,  of  humidity.     If  we  wish  to 


have  the  greatest  possible  homogeneity  in  both  directions, 
it  is  advisable  to  increase  the  number  of  plies  to  the  ut- 
most, decreasing  their  thickness;  this  also  makes  the  joining 
more  easy  by  means  of  screws  or  nails,  because  the  veneer 
offers  a  much  better  hold. 

Considerations  analogous  to  those  given  for  the  density 
of  wood,  lead  to  the  conclusion  that,  wishing  to  attain  a 
better  resistance  in  bending,  it  is  preferable  to  use  plies 
of  low  density  for  the  core.  In  fact,  the  weight  being 
the  same,  the  thickness  of  the  panels  will  be  inversely 
proportional  to  the  density;  but  the  moment  of  inertia, 
and  consequently  the  resistance  to  column  loads  are  pro- 
portional to  the  cube  of  the  thickness;  we  see,  therefore, 
the  great  advantage  of  having  the  core  made  of  light  thick 
material. 

Light  material  would  also  be  convenient  for  the  faces,  but 
they  must  also  satisfy  the  condition  of  not  being  too  soft, 
in  order  to  withstand  the  wear  due  to  external  causes. 

In  Tables  18  and  19  we  have  gathered  some  of  the  tests 


MATERIALS 


243 


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244 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


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MA  TERIALS 


245 


Table    20. — Haskelite    Designkng    Table 
Not  Sanded 
Haskelite  Research  Laboratories- 


FOH    Three-ply    Panels 
-Report  No.  109 


Nominal 
thickness 
of  panel 


Faces 


Thickness  and  kind 
of  wood 


Thickness  and  kind 
of  wood 


ViQ  in. 
Spanish  cedar. . 
Spanish  cedar . . 
Spanish  cedar. . 
Spanish  cedar. . 
IVIex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 

Maple 

Maple 

Maple 

Maple 

Birch 

Birch 

Birch 

Birch 


Vio  in. 
Spanish  cedar  .  . 
Spanish  cedar . . . 
Spanish  cedar. . . 
Spanish  cedar. . . 
Spanish  cedar. . . 
Spanish  cedar.  . . 
Mex.  mahogany. 
Mex.  mahogany. 
Mex.  mahogany. 
Mex.  mahogany. 
Mex.  mahogany. 
Mex.  mahogany. 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 


'4o  m. 
Spanish  cedar.  .  . 
Mex.  mahoganj- 

Maple 

Birch 

Spanish  cedar.  .  . 
Mex.  mahogany. 

Maple 

Birch 

Spanish  cedar ,  .  . 
Mex.  mahogany. 

Maple 

Birch 

Spanish  cedar .  .  . 
Mex.  mahogany. 

Maple 

Birch 


Approxi- 
mate 
weight 


Lb.  per 
100  sq.  ft. 


-Approximate 

strength,  lb.  per 

in.  of  width 

Along  I  Along 
face  I  core 
grain     j     grain 


>20  in- 

Bassvvood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Spanish  cedar. . . 

Poplar 

Mex.  mahogany. 

Maple 

Birch 

Basswood 

Spanish  cedar . . . 

Poplar 

Mex.  mahogany. 

Maple 

Pirch 

Basswood 

Spanish  cedar . . . 

Poplar 

Mex.  mahogany. 

Maple 

Birch 


21 
22 
24 
25 
22 
23 
20 
26 
27 
28 
31 
31 
28 
28 
31 
31 


26 
27 
27 
28 
33 
33 
27 
28 
28 
29 
34 
35 
32 
33 
33 
34 
39 
40 
33 
33 
34 
35 
40 
40 


400 
400 
400 
400 
550 
550 
550 
550 
600 
600 
600 
600 
820 
820 
820 
820 


200 
270 
300 
410 
200 
270 
300 
410 
200 
270 
300 
410 
200 
270 
300 
410 


400 

500 

400 

400 

400 

650 

400 

550 

400 

600 

400 

820 

550 

500 

550 

400 

550 

650 

550 

550 

550 

600 

550 

820 

600 

500 

600 

400 

600 

650 

600 

550 

600 

600 

600 

820 

820 

500 

820 

400 

820 

650 

820 

550 

820 

600 

820 

820 

246 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table   21. — Haskelite    Designing    Table    for    Three-ply    Panels — 

Not  Sanded 

Haskelite  Research  Laboratories — Report  No.  109 


Nominal 
thickness 
of  panel 


0.121  in. 


Thickness  and  kind 
of  wood 


Ms  in. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 


Core 


Approxi- 
mate 
weight 


Approximate 

strength,  lb.  per 

in.  of  width 


Thickness  and  kind 
of  wood 


Ho  in. 

Basswood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Spanish  cedar. . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 


Lb.  per 
100  sq.  ft. 

Along 
face 
grain 

31 

570 

32 

570 

32 

570 

33 

570 

38 

570  1 

38 

570  ! 

33 

790 

33 

790 

34 

790 

35 

790 

40 

790 

40 

790 

40 

860 

41 

860 

41 

860 

42 

860 

47 

860 

48 

860 

40 

1180 

41 

1180 

42 

1180 

42 

1180 

47 

1180 

48 

1180 

Along 
core 
grain 


500 
400 

650 
550 
600 
820 
500 
400 
650 
550 
600 
820 
500 
400 
650 
550 
600 
820 
500 
400 
650 
550 
600 
820 


made  at  the  ''Forest  Product  Laboratory;"  the  veneers 
to  which  these  tests  refer  were  all  three  pUes  of  the  same 
thickness  and  the  grain  of  successive  pUes  was  at  right 
angles.  All  material  was  rotary  cut.  Perkins'  glue  was  used 
throughout.  Eight  thicknesses  of  plies,  from  %o"  to  %" 
were  tested. 

In  Tables  20  to  29  are  quoted  the  characteristics  of 
three-ply  panels  of  the  Haskehte  Mfg.  Corp.,  Grand  Rapids, 
Michigan. 


MATERIALS 


247 


Table   22. — Haskelite    Designing    Table    for   Three-ply    Panels — 

Not  Sanded 

Haskehte  Research  Laboratories — Report  No.  109 


Nominal 
thickness 

Faces 

1 

Core 

Approxi- 
mate 
weight 

Approximate 

strength,  lb.  per 

in.  of  width 

of  panel 

Thickness  and  kind 
of  wood 

Thickness  and  kind 
of  wood 

Lb.  per 
100  sq.  ft. 

Along 
face 
grain 

Along 
core 
grain 

3^8  in. 
Spanish  cedar. . .  . 

Spanish  cedar 

Spanish  cedar .... 
Spanish  cedar .... 
Spanish  cedar .... 

Spanish  cedar 

Mex.  mahogany . . 
Mex.  mahogany. . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 

He  in. 

Basswood 

Spanish  cedar 

Poplar 

33 

34 
35 
36 
42 
43 
35 
36 
37 
38 
44 
45 
42 
43 
44 
45 
51 
52 
43 
44 
44 
46 
52 
52 

570 
570 

570 

570 

570 

570 

790 

790 

790 

790 

790 

790 

860 

860 

860 

860 

860 

860 

1180 

1180 

1180 

1180 

1180 

1180 

620 
500 
810 

Mex.  mahogany.. 

690 
750 

Birch 

1030 

Basswood 

Spanish  cedar 

Poplar 

620 
500 
810 

Mex.  mahogany . . 
Maple 

690 
750 

0.133  in. 

Birch 

1030 

Basswood 

Spanish  cedar. . . . 
Poplar 

620 

Maple 

Maple 

Maple 

Maple 

500 
810 

Mex.  mahogany.. 

Maple 

Birch 

690 
750 

Maple 

Birch 

1030 

Basswood 

Spanish  cedar 

Poplar 

620 

Birch 

Birch 

500 
810 

Birch 

Birch 

Mex.  mahogany . . 
Maple 

690 
750 

Birch 

Birch . . . 

1030 

One  of  the  best  veneers  for  aviation  is  one  obtained  with 
spruce  plies;  this  is  easily  understood  if  we  consider  the 
low  density  of  spruce. 


D.    VARIOUS  MATERULS 


(a)  Fabrics. — Fabrics  used  for  covering  airplane  wings 
are  generally  of  Unen  or  cotton,  though  sometimes  of  silk. 
The  fabric  is  characterized  by  its  resistance  to  tension  and 


248 


MHI'l.ASK  DESICX  AS  I)  COS  STRICT  ION 


Table    23. — Haskelite    Designing    Table    for    Three-ply    Panels — 

Not  Sandeu 

Haskolito  Research  Laboratories — Report  No.  109 


Cor 


Nominal 
thickness 
of  panel 


Approxi-  Approximate 

mate  strength,  lb.  per 

weight 


Thickness  and  kind 
of  wood 


Thickness  and  kind 
of  wood 


Lb.  per 
100  sq.  ft 


Along 
face 
grain 


Along 
core 
grain 


0  154  in. 


Ks  in- 
Spanish  cedar . . .  . 
Spanish  cedar. . .  . 
Spanish  cedar. . .  . 
Spanish  cedar . . .  . 
Spani.sli  cedar. . . 
Spanish  cedar. . .  . 
Spanish  cedar . . .  . 
Mex.  mahogany. 
Mex.  mahogany . 
Mex.  mahogany . 
Mex.  mahogany . 
Mex.  mahogany. 
Mex.  mahogany. 
Mex.  mahogany . 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 


712  in- 

Basswood 

Redwood 

Spanisli  cedar . . . 

Poplar 

Mex.  mahogany. 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar.  .  . 

Poplar 

Mex.  mahogany. 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar .  .  . 

Poplar 

Mex.  mahogany. 
Maple 


Maple j  Birch 

Birch Basswood 

Birch Redwood 

Birch I  Spanish  cedar. . 

Birch I  Poplar 

Birch Mex.  mahogany 

Birch Maple 

Birch Birch 


38 
38 
39 
40 
41 
50 
50 
40 
40 
41 
42 
43 
51 
52 
47 
47 
48 
49 
50 
58 
59 
47 
47 
49 
49 
51 
59 
GO 


570 
570 
570 
570 
570 
570 
570 
790 
790 
790 
790 
790 
790 
790 
860 
860 
860 
860 
860 
860 
860 
1180 
1180 
1180 
1180 
1180 
1180 
1180 


830 

710 

670 

1080 

920 

1000 

1380 

830 

710 

670 

1080 

920 

1000 

1380 

830 

710 

670 

1080 

920 

1000 

1380 

830 

710 

670 

1080 

920 

1000 

1380 


MATERIAL,^ 


249 


Table    24. — Haskeltte    Designing    Table    koh    Three-ply 
Not  Sanded 
Haskelite  Research  Laboratories — Report  No.  109 


Panels- 


Nominal 
thickness 
of  panel 


Faces 


Thickness  and  kind 
of  wood 


Thickness  and  kind 
of  wood 


Approxi- 
mate 
weight 


Lb.  per  . 
100  sq.  ft. 


Approximate 

strength,  lb.  per 

in.  of  width 


Along 
face 
grain 


Along 
core 
grain 


0.183  in. 


}4o  in. 
Spanish  cedar. . .  . 
Spanish  cedar . . .  . 
Spanish  cedar .... 
Spanish  cedar .... 
Spanish  cedar .... 
Spanish  cedar .... 
Spanish  cedar .... 
Mex.  mahogany.  . 
Mex.  mahogany.  . 
Mex.  mahogany .  . 
Mex.  mahogany.  . 
Mex.  mahogany.  . 
Mex.  mahogany . . 
Mex.  mahogany.  . 

Maple 

Maple • 

Maple 

Maple 

Maple 

Maple 

Maple 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 


Basswood 

Redwood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar .  . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 


800 

800 

800 

800 

800 

800 

800 

1100 

1100 

1100 

1100 

1100 

1100 

1100 

1200 

1200 

1200 

1200 

1200 

1200 

1200 

1650 

1650 

1650 

1650 

1650 

1650 

1650 


830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 


250 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table   25. — Haskelite    Desigxing    Table    fok    Three-ply 
Not  Sanded 
Haskelite  Research  Laboratories — Report  No.  109 


Panels — 


Nominal 
thickness 
of  panel 


Core 


Thickness  and  kind 
of  wood 


Thickness  and  kind 
of  wood 


Approxi- 
mate 
weight 


Lb.  per 
100  sq.  ft. 


Approximate 

strength,  lb.  per 

in.  of  width 


Along 
face 
grain 


Along 
core 
grain 


0.208  in. 


Vie  in. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Max.  mahogany. . 
Mex.  mahogany. , 
Max.  mahogany . . 
Mex.  mahogany . . 
Max.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany. . 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 


3- {2  in. 

Basswood 

Redwood 

Spanish  cedar .... 

Poplar 

Mex.  mahogany. . 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar. . .  . 

Poplar 

Mex.  mahogany. . 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar. . .  . 

Poplar 

Mex.  mahogany. . 

Maple 

Birch 


Birch '  Basswood , 

Birch i  Redwood 

Birch i  Spanish  cedar . . 

Birch Poplar. 

Birch 

Birch 

Birch 


Mex.  mahogany. 

Maple 

Birch 


1000 
1000 
1000 
1000 
1000 
1000 
1000 
1370 
1370 
1370 
1370 
1370 
1370 
1370 
1500 
1500 
1500 
1500 
1500 
1500 
1500 
2060 
2060 
2060 
2060 
2060 
2060 
2060 


830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 


MATERIALS 


251 


Table   26. — Haskelite    Designing    Table    for    Three-ply    Panels- 

NoT  Sanded 

Haskelite  Research  Laboratories — Report  No.  109 


Nominal 
thickness 

Faces 

Core 

Approxi- 
mate 
weight 

Approximate 

strength,  lb.  per 

in.  of  width 

of  panel 

Thickness  and  kind 
of  wood 

Thickness  and  kind 
of  wood 

Lb.  per 
100  sq.  ft. 

Along        Along 
face           core 
grain         grain 

He  in. 

Spanish  cedar 

Spanish  cedar .... 
Spanish  cedar. . .  . 
Spanish  cedar. . .  . 

Spanish  cedar 

Spanish  cedar. . .  . 
Spanish  cedar .... 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Mex.  mahogany . . 
Maple 

}s  in. 

Basswood 

Redwood 

Spanish  cedar 

Poplar 

58 
58 

61 
62 
64 
76 
77 
62 
62 
64 
65 
67 
79 
80 
74 
74 
76 
77 
79 
92 
93 
75 
75 
77 
78 
80 
93 
94 

1000 
1000 
1000 

1000 
1000 
1000 
1000 
1370 
1370 
1370 
1370 
1370 
1370 
1370 
1500 
1500 

1250 
1060 
1000 
1620 

Mex.  mahogany . . 
Maple 

1370 
1500 

Birch 

2060 

Basswood 

Redwood 

Spanish  cedar 

Poplar 

1250 
1060 
1000 
1620 

Mex.  mahogany . . 
Maple 

1370 
1500 

0.250  in. 

Birch 

2060 

Basswood 

Redwood 

Spanish  cedar. . .  . 

Poplar 

Mex.  mahogany . . 
Maple 

1250 

Maple 

in^n 

Maple 

Maple 

Maple 

Maple 

Maple 

Birch  

1500       1000 
1500     :   1620 
1500        1370 
1500       i-'inn 

Birch 

1500 
2060 
2060 
2060 
2060 
2060 
2060 
2060 

2060 

Basswood 

Redwood 

Spanish  cedar .... 
Poplar 

1250 

Birch 

1060 

Birch 

1000 

Birch 

1620 

Birch 

Mex.  mahogany.. 
Maple 

1370 

Birch 

Birch 

1500 

Birch 

2060 

252 


AIIiPLANE  DESIGN  AND  CONSTRICTION 


Table    27. — Haskelite    Designing    Table    for    Thkee-ply     Panels — 

Not  Sanded 

Haskelite  Research  Laboratorios — Report  No.  109 


Nominal 
thickness 
of  panel 


Faces 


Thickness  and  kind 
of  wood 


Core 


Thickness  and  kind 
of  wood 


Approximate 

strength,  lb.  per 

in.  of  width 


Along 
face 
grain 


Along 

core 

grain 


0.250  in. 


H2  in. 
Spanish  cedar. 
Spanish  cedar. 
S|)anish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Mex.  mahogany.  . 
Mox.  mahogany . 
Mex.  mahogany. 
Mex.  mahogany . 
Mex.  mahogany . 
Mex.  mahogany . 
Mex.  mahogany . 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 


H2  in. 

Basswood 

Redwood 

Spanish  cedar. . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar. . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar. . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar .  . 

Poplar 

Mex.  mahogany 

Maple 

Birch 


1330 
1330 
1330 
1330 
1330 
1330 
1330 
1830 
1830 
1830 
1830 
1830 
1830 
1830 
2000 
2000 
2000 
2000 
2000 
2000 
2000 
2750 
2750 
2750 
2750 
2750 
2750 
2750 


830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

1080 

920 

1000 

1370 

830 

710 

670 

lOSO 

920 

1000 

1370 


MATERIALS 


253 


Table    28. — Haskelite    Designing    Table    p-or    Three-ply     Panels — 

Not  Sanded 

Haskelite  Research  Laboratories — Report  No.  109 


Nominal 
thickness 

P„e. 

Core 

Approxi- 
mate 
weight 

Approximate 

strength,  lb.  per 

in.  of  width 

of  panel 

Thickness  and  kind 
of  wood 

Thickness  and  kind 
of  wood 

Lb.  per 
100  sq.  ft. 

Along 
face 
grain 

Along 
core 
grain 

H.  in. 
Spanish  cedar .... 
Spanish  cedar.  .  .  . 
Spanish  cedar.  .  .  . 
Spanish  cedar .... 

Spanish  cedar 

Spanish  cedar .... 
Spanish  cedar .... 
Mex.  mahogany.  . 
Mex.  mahogany .  . 
Mex.  mahogany .  . 
Mex.  mahogany.  . 
Mex.  mahogany . . 
Mex.  mahogany. . 
Mex.  mahogany. . 

H  in. 

Basswood 

Redwood 

Spanish  cedar 

Poplar. . . . 

68 
68 

70 
71 
73 
86 
87 
72 
72 
74 
75 
77 
90 
91 
89 
89 
91 
92 
94 
106 
107 
90 
90 
92 
93 
95 
108 
109 

1330 

1330 
1330 
1330 
1330 
1330 
1330 
1830 
1830 
1830 
1830 
1830 
1830 
1830 
2000 
2000 
2000 
2000 
2000 
2000 
2000 
2750 
2750 
2750 
2750 
2750 
2750 
2750     i 

1250 
1060 
1000 
1620 

Mex.  mahogany.  . 
Maple 

1370 
1500 

Birch   . 

2060 

Basswood 

Redwood 

Spanish  cedar. . .  . 
Poplar . . . 

1250 
1060 
1000 
1620 

Mex.  mahogany . . 
Maple 

1370 
1500 

Birch 

2060 

0.291  in. 

Basswood 

Redwood 

Spanish  cedar .... 

Poplar 

Mex.  mahogany.  . 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar. . .  . 

Poplar 

Mex.  mahogany.  . 

Maple 

Birch 

1250 
1060 

Maple 

Maple 

1000 
1620 

Maple 

Maple 

1370 
1500 

Maple. 

2060 

Birch 

1250 

Birch 

Birch 

1060 
1000 

Birch 

Birch 

1620 
1370 

Birch 1 

Birch 

1500 
20(0 

254 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table    29. — IIaskkliti:    Designing    Table    for    Three-ply     Panels — 

Not  Sanded 

Haskelite  Research  Laboratories — Rejxtrt  No.  109 


Nominal 
thickness 
of  panel 


Faces 


Thickness  and  kind 
of  wood 


Thickness  and  kind 
of  wood 


Appi 


Approximate 
strength,  lb.  per 
weight  in.  of  width 


Lb.  per 
100  sq.  ft. 


Along 
face 
grain 


Along 
core 
grain 


0.375  in. 


Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Spanish  cedar. 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 
Mex.  mahogany 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Maple 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 

Birch 


H  iri. 

Basswood 

Redwood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar. . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar .  . 

Poplar 

Mex.  mahogany 

Maple 

Birch 

Basswood 

Redwood 

Spanish  cedar . . 

Poplar 

Mex.  mahogany 

Maple 

Birch 


87 

87 

89 

90 

92 

104 

105 

93 

93 

95 

96 

98 

111 

112 

118 

118 

120 

121 

123 

136 

137 

120 

120 

122 

123 

125 

138 

139 


2000 
2000 
2000 
2000 
2000 
2000 
2000 
2750 
2750 
2750 
2750 
2750 
2750 
2750 
3000 
3000 
3000 
3000 
3000 
3000 
3000 
4120 
4120 
4120 
4120 
4120 
4120 
4120 


1250 
1060 
1000 
1620 
1370 
1500 
2060 
1250 
1060 
1000 
1620 
1370 
1500 
2060 
1250 
1060 
1000 
1620 
1370 
1500 
2060 
1250 
1060 
1000 
1620 
1370 
1500 
2060 


MATERIALS 


255 


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—  ^  O  •*  iC  ■>* 
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t^  M  fC  t>.  e<3  lO 
IN  CC  »0  CO  -^  CD 

J  J  J  J  J  J 
C^  Cq  C^  C^  CM  C^ 

IC  o 
CO  d 

J  7 

00  00 

00  CO  O  00  CO  o 
00  t^  (N  00  t^  t^ 

(M  IC  O  IM  lO  00 


(M  CC 
00  t^ 


£1 


Tf  I>  O  00  (M  t^ 
lO  CO  O  O  t^  05 

J  J  J  J  J  J 
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f  f 

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H^  o 


00  CD  O  00  CD  O 
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C<l  lO  O  iM  lO  00 


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o  o  o 

CO  t^  O 

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CQ  CQ  cq  P3  c2  cc 


»0  CD  t^  00  05  O 


256 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


to  tearing,  both  in  the  direction  of  the  woof  and  the  warp, 
and  by  its  weight  per  square  foot. 

Table  30  gives  the  characteristics  of  several  types  of 
fabric.  In  this  table  we  find  for  various  types  the  weight 
per  square  yard,  the  resistance  in  pounds  per  square  yard 
(referring  to  both  woof  and  warp)  and  the  ratio  between  the 
resistance  and  weight.  We  see  that  silk  is  the  most  con- 
venient material  for  lightness;  the  cost  of  this  material  with 
respect  to  the  gain  in  weight  is  so  high  as  to  render  its  use 
impractical. 

Fabric  must  be  homogeneous  and  the  difference  between 
the  resistance  in  warp  and  woof  should  not  exceed  10  per 


Fig.  152. 

cent,  of  the  total  resistance;  in  fact  the  fabric  on  the 
wings  is  so  disposed  that  the  threads  are  at  45°  to  the  ribs, 
thus  working  equally  in  both  directions  and  having  con- 
sequently the  same  resistance:  in  the  calculations,  there- 
fore, the  minor  resistance  should  be  taken  as  a  basis;  the 
excess  of  resistance  in  the  other  direction  resulting  only  in  a 
useless  weight. 

(b)  Elastic  Cords. — For  landing  gears  the  so-called  elastic 
cord  is  universally  adopted  as  a  shock  absorber. 

It  is  made  of  multiple  strands  of  rubber  tightly  incased 
within  two  layers  of  cotton  braid  (Fig.  152).  Both  the  in- 
ner and  outer  braids  are  wrapped  over  and  under  with  three 
or  four  threads.  The  rubber  strands  are  square  and  are 
made  of  a  compound  containing  not  less  than  90  per  cent. 


MATERIALS 


257 


of  the  best  Para  rubber.     The  size  of  a  single  strand  is 
between  0.05  and  0.035  inch. 

The  rubber  strands  are  covered  with  cotton  while  they 
are  subjected  to  an  initial  tension,  in  order  to  increase  the 


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?50 


300        350 


work  that  the  elastic  can  absorb.     The  diagrams  of  Figs. 
153  and  154  show  this  clearly. 

Fig.  153  gives  the  diagram  of  work  of  a  mass  of  rubber 
strands  without  cotton  wrapping  and  without  initial  tension. 


258 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Fig.  154  gives  the  diagram  of  the  same  mass  of  rubber 
strands  with  an  initial  tension  of  127  per  cent.,  and  with 
the  cotton  wrapping. 

In  general,  the  elongation  is  limited  for  structural  rea- 
sons; let  us  suppose  for  instance,  that  an  elongation  of  150 
per  cent,  be  the  maximum  possible.  It  is  then  interesting 
to  calculate  the  work  which  can  be  absorbed  by  1  lb.  of 
elastic  cord  having  initial  tension  and  cotton  wrapping 
and  to' compare  it  to  that  which  can  be  absorbed  by  1  lb.  of 
elastic  cord  without    initial    tension  and  without  cotton 


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200  250  300 

Loading, Pounds. 
Fig.   154. 


wrapping.  The  work  can  be  easily  calculated  by  measuring 
the  shaded  areas  in  Figs.  153  and  154.  Naturally  to  do 
this  it  is  necessary  to  translate  the  per  cent,  scale  of  elonga- 
tion into  inches,  which  is  easy  when  the  weight  per  yard  is 
knowm. 

For  150  per  cent,  of  elongation  the  work  absorbed  by 
1  lb.  of  elastic  cord  without  initial  tension  and  without 
cotton  wrapping  is  1280  Ib.-in.;  while  that  absorbed  by 
elastic  cord  with  127  per  cent,  of  initial  elongation  is  equal  to 
20,200  Ib.-in.;  that  is,  in  the  second  case  a  work  about 
16  times  greater  can  be  absorbed  with  the  same  weight. 
This  shows  the  great  convenience  in  using  elastic  cords 
with  a  high  initial  tension. 


MATERIALS  259 

(c)  Varnishes. — ^Varnishes  used  for  airplane  fabrics  are 
divided  into  two  classes:  stretching  varnishes  (called 
"dope"),  and  finishing  varnishes. 

The  former  are  intended  to  give  the  necessary  tension 
to  the  cloth  and  to  make  it  waterproof,  increasing  at  the 
same  time  its  resistance.  The  finishing  varnishes  which 
are  applied  over  the  stretching  varnishes  have  the  scope  of 
protecting  these  latter  from  atmospheric  disturbances,  and 
of  smoothing  the  wing  surfaces  so  as  to  diminish  the  resist- 
ance due  to  friction  in  the  air. 

The  stretching  varnishes  are  generally  constituted  of  a 
solution  of  cellulose  acetate  in  volatile  solvents  without 
chlorine  compounds.  The  cellulose  acetate  is  usually  con- 
tained in  the  proportion  of  6  to  10  per  cent.  The  solvents 
mixtures  must  be  such  as  not  to  alter  the  fabrics  and  not 
to  endanger  the  health  of  men  who  apply  the  varnish. 

The  use  of  gums  must  be  absolutely  excluded  because 
they  conceal  the  eventual  defects  of  the  cellulose  film.  A 
good  stretching  varnish  must  render  the  cloth  absolutely 
oil  proof,  and  will  increase  the  weight  of  the  fabric  by  30 
per  cent,  and  its  resistance  by  20  to  30  per  cent. 

Finally  it  should  be  noted  that  it  is  essential  for  the  var- 
nish to  increase  the  inflammability  of  the  fabric  as  little  as 
possible;  precisely  for  this  reason  the  cellulose  nitrate 
varnish  is  used  very  seldom,  notwithstanding  its  much 
lower  cost  when  compared  with  cellulose  acetate. 

In  general  for  linen  and  cotton  fabrics  three  to  four  coats 
of  stretching  varnish  are  sufficient;  for  silk  instead,  it  is 
preferable  to  give  a  greater  number  of  coats,  starting  with 
a  solution  of  2  to  3  per  cent,  of  acetate  and  using  more 
concentrated  solutions  afterward. 

The  finishing  varnishes  are  used  on  fabric  which  have 
already  been  coated  with  the  stretching  varnishes.  These 
have  as  base  linseed  oil  with  an  addition  of  gum,  the  whole 
being  dissolved  in  turpentine. 

A  good  finishing  varnish  must  be  completely  dry  in  less 
than  24  hours,  presenting  a  brilUant  surface  after  the  drying, 


260  AIRPLANE  DESKIN  AND  CONSTRUCTION 

resistant  to  crumpling,  and  able  to  withstand  a  wash  with  a 
solution  of  laundry  soap. 

{d)  Glues. — Glues  are  greatly  used  both  in  manufac- 
turing propellers  and  veneers. 

Beside  having  a  resistance  to  shearing  superior  to  that  of 
wood,  a  good  glue  must  also  resist  humidity  and  heat. 
There  are  glues  which  are  applied  hot  (140°F.),  and  those 
which  are  applied  cold. 

A  good  glue  should  have  an  average  resistance  to 
shearing  of  2400  lb.  per  sq.  in. 


CHAPTER  XVII 
PLANNING  THE  PROJECT 

When  an  airplane  is  to  be  designed,  there  are  certain 
imposed  elements  on  the  basis  of  which  it  is  necessary  to 
conduct  the  study  of  the  other  various  elements  of  the 
design  in  order  to  obtain  the  best  possible  characteristics. 

Airplanes  can  be  divided  into  two  main  classes:  war  air- 
planes and  mercantile  airplanes. 

In  the  former,  those  qualities  are  essentially  desired  which 
increase  their  war  efficiency,  as  for  instance:  high  speed, 
great  climbing  power,  more  or  less  great  cruising  radius, 
possibility  of  carrying  given  military  loads  (arms,  muni- 
tions, bombs,  etc.),  good  visibihty,  facility  in  installing 
armament,  etc. 

For  mercantile  airplanes,  on  the  contrary,  while  the  speed 
has  the  same  great  importance  a  high  climbing  power  is 
not  an  essential  condition;  but  the  possibility  of  transport- 
ing heavy  useful  loads  and  great  quantities  of  gasoline  and 
oil,  in  order  to  effectuate  long  journeys  without  stops, 
assumes  a  capital  importance. 

WTiatever  type  is  to  be  designed,  the  general  criterions 
do  not  vary.  Usually  the  designer  can  select  the  type  of 
engine  from  a  more  or  less  vast  series;  often  though,  the 
type  of  motor  is  imposed  and  that  naturally  limits  the 
fields  of  possibility. 

Rather  than  exposing  the  abstract  criterions,  it  is  more 
interesting  to  develop  summarily  in  this  and  the  following 
chapters,  the  general  outline  of  a  project  of  a  given  type 
of  airplane,  making  general  remarks  which  are  applicable 
to  each  design  as  it  appears.  In  order  to  fix  this  idea, 
let  us  suppose  that  we  wish  to  study  a  fast  airplane  to  be 
used  for  sport  races. 

261 


262  AIRPLANE  DESIGN  AND  CONSTRUCTION 

The  future  aviation  races  will  certainly  be  marked  by 
imposed  limits,  which  may  serve  to  stimulate  the  designers 
of  airplanes  as  well  as  of  engines  towards  the  increase  of 
efficiency  and  the  research  of  all  those  factors  which  make 
flight  safer. 

For  instance,  for  machines  intended  for  races  the  ultimate 
factor  of  safety,  the  minimum  speed,  the  maximum  hourly 
consumption  of  the  engine,  etc.,  can  be  imposed. 

The  problem  which  presents  itself  to  the  designer  may  be 
the  following :  to  construct  an  airplane  having  the  maximum 
possible  speed  and  also  embodying  the  following  qualities: 

1.  A  coefficient  of  ultimate  resistance  equal  to  9. 

2.  Capable  of  sustentation  at  the  minimum  speed  of  75 
m.p.h. 

3.  Capable  of  carrying  a  total  useful  load  of  180  lb.  (pilot 
and  accessories),  beside  the  gasoUne  and  oil  necessary  for 
three  hours  flight. 

4.  An  engine  of  which  the  total  consumption  in  oil  and 
gasoHne  does  not  surpass  180  lb.  per  hour  when  running 
at  full  power. 

Let  us  call  W  the  total  weight  in  pounds  of  the  airplane 
at  full  load,  A  its  sustaining  surface  in  sq.  ft.,  W^  the  useful 
load  in  pounds,  P  the  power  of  the  motor  in  horsepower, 
and  C  the  total  specific  consumption  of  the  engine  in  oil 
and  gasoline. 

Remembering  that  in  normal  flight 

W  =  10-'\AV' 

since  the  condition  is  imposed  that  the  airplane  sustain 
itself  for  V  =  75  m.p.h.,  we  must  have 
W 

-J-   <   0.56  Xmax. 

that  is,  the  load  per  square  foot  of  wing  surface  will  have  to 
equal  ^%qq  of  the  maximum  value  Xn,ax.  which  it  is  possible 
to  obtain  with  the  aerofoil  under  consideration. 
The  total  useful  load  will  equal 

W^  =  180  +  3cF 


PLANNING  THE  PROJECT  263 

Let  US  call  Wp  the  weight  of  the  motor  including  the 
propeller,  W„  the  weight  of  the  radiator  and  water,  W^ 
the  weight  of  the  airplane. 
Then 

W  =  W^  +  W,  +  W,  +  W^  (1) 

Calling  p  the  weight  of   the   engine  propeller  group  per 
horsepower  we  will  have 

Wp  =  pP 
The  weight  of  the  radiator  and  water,  by  what  we  have 
said  in  Chapter  V,  can  be  assumed  proportional  to  the  power 
of  the  engine  and  inversely  proportional  to  the  speed. 

As  to  the  weight  of  the  airplane,  for  airplanes  of  a  certain 
well-studied  type  and  having  a  given  ultimate  factor  of 
safety,  it  can  be  considered  proportional  to  the  total 
weight;  we  can  therefore  write 

W^  =  aW 

Then  (1)  can  be  written 

W  =  ISO  -\-ScP  +  pP  +  by  +  aW 

that  is 

^  =  ^  +  r^„(3c4-P+|)  (2) 

The  machine  we  must  design  is  of  a  type  analogous  to  the 
single-seater  fighter.  Consequently  in  the  outhne  of  the 
project  we  can  use  the  coefficients  corresponding  to  that 
type. 

For  these,  the  value  of  a  is  about  0.34;  also,  expressing  V 
in  m.p.h.  we  can  take  b  =  45. 

Remembering  the  imposed  condition  that  cP  must 
not  exceed  180  lb.,  we  will  have  to  select  an  engine  having 
the  minimum  specific  consumption  r,  in  order  to  have  the 
maximum  value  of  P;  at  the  same  time  the  weight  p  per 
horsepower  must  be  as  small  as  possible. 


264 


AIRPLANE  DESKIX  A\D  CONSTRUCTION 


Let  US  suppose  that  four  types  of  engines  of  the  following 
characteristics  are  at  our  disposal: 
Table  31 


/' 
II. l» 


II).  per  II. P. 


C 


I 

250 

2.3 

0.54 

575 

135 

II 

300 

2.2 

0.53 

660 

159 

III 

350 

2.1 

0.56 

735 

196 

IV 

400 

2.0 

0  50 

800 

23G 

It  is  clearly  visible  that  engines  No.  Ill  and  No.  IV 
should  without  doubt  be  discarded  since  their  hourly  con- 
sumption is  greater  than  the  already  imposed,  180  lbs.  Of 
the  other  engines  the  more  convenient  is  undoubtedly  type 
II  for  which  the  value  of  p  is  lower. 

Then  formula  (2),  making  a  =  0.34,  P  =  300,  c  =  0.53, 
p  =  2.2,  b  =  45,  becomes 

20^  (3) 


TT^ 


1992  + 


To   determine    W  as  a   first   approximation,   let  us  re 
member  that  the  formula  of  total  efficiency  gives 

WV 


0.00248 


(4) 


and  that  for  a  machine  of  great  speed  we  can  take  r  =  2.8; 
then  making  P  =  300  we  have 

J_  ^  J)^0248  ^ 
V  840 

and  substituting  in  (3) 

W  (1  -  0.06)  =  1992 
that  is, 

W  =  2130 
Then  V  =  159  m.p.h. 
Consequently  we  can  claim;    in  the  first   approximation, 
that  the  principal  characteristics  of  our  airplane  will  be 
W  =  2130  lbs. 
F_.  =  159  m.p.h. 
F„.i„.  =  75  m.p.h. 
P  =  300  H.P. 


PLANNING  THE  PROJECT 


265 


Let  us  now  determine  the  sustaining  surface. 
We  have  seen  that  we  must  have 
W  - 

^   <    0.56    Xn,ax. 

where  X^^x.  is  the  maximum  value  it  is  practical  to  obtain. 


S     X 


l./O    ^& 1 1 1 

/ 

t 

t 

^          ^« — kIu                     Z          a 

^        /        1          ^s.                  <i  =/ 

~      b     /              1         ^"s               / 

4                ._           %J.        -^   ^^ 

_...                            /                                  f          n^ 

T  ^               /  S^ 

t            ^^i^        ^ 

1-          >^            ^ 

y           ^^£               ^< 

nc:n     ,n                                            ^                    ^^^      a1                                           ^S 

r   ^^ 

4  ^^ 

no^       c                                     fc-i 

^'i 

^  1- 

.    oi          ::^ 

n,5 


2 
Degree© 

Fig.   155. 


T5 


From  the  aerofoils  at  our  disposition,  let  us  select  one 
which,  while  permitting  the  realization  of  the  above  con- 
dition, at  the  same  time  gives  a  good  efficiency  at  maximum 


Let  us  suppose  that  we  choose  the  aerofoil  having  the 
characteristics  given  in  the  diagram  of  Fig.  155. 
Then  as  X^ax  =  14.4,  we  must  have 


266 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


■i^iair  -J 

Uf  L9S9 

^ 

WOS/9 

N. 

VO 

^ 

5i 

^ 

^ 

w 

c 

^ 

s 

1 

§ 

1 

1 

- 

oS 

OQ 

t: 

s 

§ 

^1^ 

^» 

55 

l\  X        /'^  \\/ 

i 

^ 

^ 

v  X        ^^ J^\ 

m 

S 

s 

§ 

A:  ^       ^,^''^^^0^ 

i§ 

'♦^ 

(^                        / 

t 

\                         / 

s 

<o 

ao 

\                  / 

^*^ 
^ 

\           / 

^ 

c 

«i 

s 

•5 

\    / 

ff> 

o 

«A 

ci 

CM 

N 

)\ 

oa 

1 

§ 

/  \ 

^ 

^ 

/         \ 

s 

§ 

/                \ 

§ 

? 

/                        ^ 

L -^ 

^ 

^ 

r-; 

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(0 

K 

vt> 



^ 

1 

PLANNING  THE  PROJECT  267 

W 

For  -^  =  8  and  W  =  2130  lb. 

A  =  265  sq.  ft. 

Let  us  select  a  type  of  biplane  wing  surface  adopting  a 
chord  of  65".     The  scheme  will  be  that  shown  in  Fig.  156. 

We  can  then  compile  the  approximate  table  of  weights, 
considering  the  following  groups: 

1.  Useful  Load 

Pilot 180  lb. 

Gasoline  and  oil 477  lb. 

Instruments 11  lb. 

Total 668  lb. 

2.  Engine  Propeller  Group 

Dry  engine  and  propeller 660  lb. 

Exhaust  pipes 6  lb. 

Water  in  the  engine 30  lb. 

Radiator  and  water 125  lb. 

Total 821  lb. 

3.  Wing  Truss 

Spars 100  1b. 

Ribs 26  lb. 

Horizontal  struts  and  diagonal  bracings 20  lb. 

Fittings  and  bolts 30  lb. 

Fabric  and  varnish 25  lb. 

Vertical  struts 40  lb. 

Main  diagonal  bracing 35  lb. 

Total 2761b. 

4.  Fuselage 

Body  of  fuselage 155  lb. 

Seat,  control  stick,  and  foot  bar 25  lb. 

Gasoline  tanks  and  distributing  system 40  lb. 

Oil  tanks  and  distributing  system 6  lb. 

Cowl  and  finishing 25  lb. 

Total 251  lb. 

5.  Landing  Gear 

Wheels 32  lb. 

Axle  and  spindle 25  lb. 

Struts 15  1b. 

Cables 4  lb. 

Total 76  lb. 


268 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


6.  Controls  and  Tail  Group 

Ailerons 12  lb. 

Fin 2  1b. 

Rudder 6  lb. 

Stabilizer 8  lb. 

Elevator 10  lb. 

Total  38  lb. 

We  can  then  compile  the  following  approximate  table: 

Table  32 

Donoininatioii 


Weight  in  lb. 

Per  cent 

.  of  total 

weight 

668 

31.0 

821 

38.5 

276 

13.0 

251 

12.0 

76 

3.5 

38 

2.0 

2130 

100.0 

1.  Useful  load 

2.  Engine  propeller  group. 

3.  Wing  truss 

4.  Fuselage 

5.  Landing  gear 

6.  Controls 


Total. 


A  schematic  side  view  of  the  machine  is  then  drawn  in 
order  to  find  the  center  of  gravity  as  a  first  approximation. 

In  determining  the  length  of  the  airplane,  or  better,  the 
distance  of  tail  system  from  the  center  of  gravity,  we  have 
a  certain  margin,  since  it  is  possible  to  easily  increase  or 
decrease  the  areas  of  the  stabilizing  and  control  surfaces. 
For  machines  of  types  analogous  to  those  which  we  are 
studying,  the  ratio  between  the  wing  span  and  length  usu- 
ally varies  from  0.60  to  0.70.  Since  we  have  assumed  the 
wing  span  equal  to  26.6  ft.,  we  shall  make  the  length  equal 
to  18  ft.;  that  is,  we  shall  adopt  the  ratio  0.678.  The  side 
view  (Fig.  157)  shows  the  various  masses,  with  the  excep- 
tion of  the  wings  and  landing  gear;  these  are  separately 
drawn  in  Figs.  158  and  159.  Then  with  the  usual  methods 
of  graphic  statics  we  determine  separately  the  center  of 
gravity  of  the  fuselage  (with  all  the  loads),  of  the  wing 
truss,  and  of  the  landing  gear. 

It  is  then  easy  to  combine  the  three  drawings  so  that  the 
following  conditions  be  satisfied: 

1.  That  the  center  of  gravity  of  the  whole  machine  be  on 


PLANNING  THE  PROJECT 


269 


270 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Pounds. 


Fig.  158. 


PLANNING  THE  PROJECT 


271 


Pounds 


FiQ.   159. 


272 


AIRPLAXE  DESICN  AND  CONSTRUCTION 


•spunoj 


PLANNING  THE  PROJECT  273 

the  vertical  line  passing  through  the  center  of  pressure  of 
the  wings. 

2.  That  the  axis  of  the  landing  gear  be  on  a  straight  line 
passing  through  the  center  of  gravity  and  inclined  forward 
by  14°;  that  is,  by  about  25  per  cent. 

The  superimposing  has  been  made  in  Fig.  160. 

The  ideal  condition  of  equilibrium  is  that  the  center  of 
gravity,  thus  found,  not  only  must  be  on  the  vertical  line 
passing  through  the  center  of  pressure,  but  must  also  be  on 
the  axis  of  thrust;  if  it  falls  above  the  axis  of  thrust  it  is 
advisable  that  its  distance  from  it  be  not  greater  than  4  or 
5  inches  at  the  maximum ;  if  instead  it  falls  below  the  axis 
of  thrust,  we  have  a  greater  margin  as  the  conditions  of 
stability  improve.  This  shall  be  seen  in  Chapter  XXI. 
In  our  case,  it  falls  2.5  in.  above  the  propeller  axis. 

The  center  of  gravity  having  been  approximately  de- 
termined we  can  draw  the  general  outline  (Figs.  161,  162 
and  163). 

It  is  then  necessary  to  calculate  the  dimensions  of  the 
stabiUzer,  fin,  rudder,  and  elevator.  To  do  this,  it  would 
be  essential  to  know  the  principal  moments  of  inertia  of 
the  airplane.  The  graphic  determination  of  these  moments 
is  certainly  possible  but  it  is  a  long  and  laborious  task  be- 
cause of  the  great  quantity  and  shape  of  masses  which 
compose  the  airplane. 

Practically  a  sufficient  approximation  is  reached  by  con- 
sidering the  weight  W  instead  of  the  moment  of  inertia. 
Then  calling  M  the  static  moment  of  any  control  surface 
whatever  about  the  center  of  gravity  (that  is,  the  product  of 
its  surface  by  the  distance  of  its  center  of  thrust  from  the 
center  of  gravity)  we  shall  have 


M  =  aX 


72. 


Value  a  can  be  assumed  constant  for  machines  of  the 
same  type.  Then,  having  determined  a  based  on  machines 
which  have  notably  well  chosen  control  surfaces,  it  is  easy 
to  determine  M.     Value  a  in  our  case  can  be  taken  equal 


274  AIRPLANE  DESIGN  AND  CONSTRUCTION 


Fig.  161. 


Fig.  162. 


¥ia.  163. 


PLANNING  THE  PROJECT 


275 


to  3900  for  the  ailerons,  2100  for  the  elevator,  and  2500 
for  the  rudder,  taking  as  the  units  of  measure  pounds  for 
W  and  feet  per  second  for  V. 

Then  it  is  possible  to  compile  the  following  table  where 
a  and  M  have  the  above  significance,  I  is  the  lever  arm  in 
feet  and  *S  is  the  surface  of  the  rudder  elevator  and  ailerons 
in  square  feet.  The  velocity  V  has  been  taken  equal  to 
150  M.P.H.,  i.e.  220  ft./sec. 

Table  33 


Controls 

" 

M  (cu.  ft.) 

I  (feet) 

S  (sq.  ft.) 

3900 
4100 
2400 

172 

178 
105 

8.3 
14.8 
15.6 

21.0 

Elevator     

12  0 

Rudder 

6.7 

CHAPTER  XVIII 

STATIC  ANALYSIS  OF  MAIN  PLANES  AND  CONTROL 
SURFACES 

Owing  to  the  broadness  of  the  discussion  we  shall  limit 
ourselves  to  summarily  resume  the  principal  methods 
used  in  analyzing  the  various  parts,  referring  to  the  ordi- 
nary treaties  on  mechanics  and  resistance  of  materials  for 
a  more  thorough  discussion. 

In  this  chapter  the  static  analysis  of  the  wing  truss  and  of 
the  control  surfaces  is  given. 


ELEVATION 


Fig.   164. 


0  JO  601n 

Scale  C7f  Length* 


Fig.  164  shows  that  the  structure  to  be  calculated  is  com- 
posed of  four  spars,  two  top  and  two  bottom  ones,  con- 
nected to  one  another  by  means  of  vertical  and  horizontal 
trussings. 

For  convenience  the  analysis  of  the  vertical  trussings  is 
usually  made  separately  from  the  analysis  of  the  horizontal 
ones,  and  upon  these  calculations  the  analysis  of  the  main 
beams  can  be  made. 

276 


MAIN  PLANES  AND  CONTROL  SURFACES 


277 


First  of  all  it  is  necessary  to  determine  the  system  of  the 
acting  forces.  An  airplane  in  flight  is  subjected  to  three 
kinds  of  forces:  the  weight,  the  air  reaction  and  the  pro- 
peller thrust. 

The  weight  is  balanced  by  the  sustaining  component  L, 
of  the  air  reaction;  the  propeller  thrust  is  balanced  by  the 
drag-component  D.  The  weight  and  the  propeller  thrust 
are  forces  which  for  analytical  purposes  can  be  considered 
as  applied  to  the  center  of  gravity  of  the  airplane.  The 
components  L  and  D  instead,  are  uniformly  distributed  on 

the  wing  surface.     Practically,  the  ratio  ^  assumes  as  many 


Fig.  165. 


different  values  as  there  are  angles  of  incidence.     The  maxi- 
mum value,  which  is  assumed  in  computations,  is,  usually, 

y-  =  0.25.     Thus  it  will  be  sufficient  to  study  the  distribu- 
L/ 

tion  of  L,   because,   when   this  is  known  the  horizontal 

stresses  can  immediately  be  calculated. 

Let  us  suppose  that  the  aerofoil  be  that  of  Fig.  165  and 
that  the  relative  position  of  the  spars  be  that  indicated  in 
this  figure.  The  first  step  is  to  determine  the  load  per 
linear  inch  of  the  wing.  Fig.  164  shows  that  the  linear 
wing  development  of  the  upper  wing  is  320.48  inches  while 
that  of  the  lower  wing  is  288.58  inches. 

We  know  that  the  two  wings  of  a  biplane  do  not  carry 
equally  because  of  the  fact  that  they  exert  a  disturbing 
influence  on  each  other;  in  general  the  lower  wing  carries 
less  than  the  upper  one;  usually  in  practice  the  load  per 
unit  length  of  lower  wing  is  assumed  equal  to  0.9  of  that 


278 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


of  the  upper  wing.     Then  evidently  the  load  per  linear  inch 
of  the  upper  wing  is  given  by 
2130 
320.48  +  0.9  X  288:58  ^  ^■^'^'  ^^'  P^'  ^'''^ 

and  for  the  lower  wing  it  is  given  by 

0.9  X  3.66  =  3.29  lb.  per  inch 

From  these  linear  loads  we  must  deduct  the  weight  per 
linear  inch  of  the  wing  truss,  because  this  weight,  being 


029  I  =18.85  In. 


^S§^ 


ZiSS 


-  0.43  L 


^M 


^ 


Fig.  166. 


applied  in  a  directly  opposite  direction  to  the  air  reaction, 
decreases  the  value  of  the  reaction.  In  our  case  the  figured 
weight  of  the  wdng  truss  is  276  lb.;  thus  the  weight  per 
linear  inch  to  be  subtracted  from  the  preceding  values  will 
be  0.45  lb.  per  linear  inch. 

We  shall  then  have  ultimately: 

Upper  wing  loading 3.21  lb.  per  linear  inch 

Lower  wing  loading 2.84  lb.  per  linear  inch 

Knowing  these  loads,  it  is  possible  to  calculate  the  dis- 
tribution of  loading  upon  the  front  spars  and  upon  the  rear 
spars.  For  this  it  is  necessary  to  know  the  law  of  variation 
'  of  the  center  of  thrust. 


MAIN  PLANES  AND  CONTROL  SURFACES  279 

It  is  easily  understood  that  when  the  center  of  thrust 
is  displaced  forward,  the  load  of  the  front  spar  increases, 
and  that  of  the  rear  spar  decreases;  and  that  the  contrary 
happens  when  the  center  of  thrust  is  displaced  backward. 
We  shall  suppose  that  in  our  case  the  center  of  thrust  has 
a  displacement  varying  from  29  per  cent,  to  37  per  cent, 
of  the  wing  cord  (Fig.  166).  In  the  first  case  the  front 
spar  will  support  0.62  of  the  total  load  and  the  rear  spar 
will  support  0.38;  in  the  second  case  these  loads  will  be 
respectively  0.43  and  0.57  of  the  total  load. 

Thus  the  normal  loads  per  linear  inch  of  the  four  spars 
can  be  summarized  as  follows: 

Front  spar  upper  wing 1.98  lb.  per  inch 

Rear  spar  upper  wing 1.82  lb.  per  inch 

Front  spar  lower  wing 1.75  lb.  per  inch 

Rear  spar  lower  wing 1.62  lb.  per  inch 

Practically  it  is  convenient  to  make  the  calculations 
using  the  breaking  load  instead  of  the  normal  load;  in  fact 
there  are  certain  stresses  which  do  not  vary  proportionally 
to  the  load  but  follow  a  power  greater  than  unity,  as  we 
shall  see  presently.  In  our  case,  as  the  coefficient  must  be 
equal  to  10,  the  breaking  load  must  be  equal  to  10  times 
the  preceding  values. 

We  can  then  initiate  the  calculation  of  the  various  trusses 
which  make  up  the  structure  of  the  wings.  We  shall  proceed 
in  the  following  order,  computing: 

(a)  bending  moments,  shear  stresses  and  spar  reactions 
at  the  supports.  Determination  of  the  neutral  curve  of 
the  spars 

(6)  front  and  rear  vertical  trusses 

(c)  upper  and  lower  horizontal  trusses 

(d)  unit  stresses  in  the  spars. 

(a)  The  spars  can  be  considered  as  uniformly  loaded 
continuous  beams  over  several  supports.  In  our  case  there 
are  four  supports  for  the  upper  spars  as  well  as  for  the 
lower  ones;  the  uniformly  distributed  loadings  are  the 
preceding. 


280 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Let  US  note  first,  that  in  our 
bution  of  the  spans  of  the  rear 
spans  of  the  front  spars;  thus 
the  front  and  rear  spars  is  in 
It  suffices  then  to  calculate  the 
stresses  and  the  reactions  at 
spars;  the  same  diagrams,  by 
can  be  used  for  the  rear  spars, 
ing  for  the  rear  spars  is  equal 
spars. 


case  as  in  others,  the  distri- 
spars  is  equal  to  that  of  the 
the  only  difference  between 
the  load  per  unit  of  length, 
bending  moments,  the  shear 
the  supports  for  the  front 
a  proper  change  of  scales, 
In  our  case,  the  unit  load- 
to  0.92  of  that  for  the  front 


.1 

.         ■4S67'    . 

8$  76' 

4^6-        , 

e97e' 

,          4S67'   J 

°i         i 

1 

r  r 

r  r    i' 

1         i 

K 

1     1 
i 

i  "1^ 

IN         i 

^^-•'•^!                   'V 

k 

N"' 

-r  iV 

!  \°i        i 

A 

i        1  \ 
!        ! 

1   B 

V 

~A 

\   \ 

!      1 

i!          1 

D 

1        1 

la,           ib, 

Im, 

!     J 

Ic,      id, 

in.     ie,            if. 

0  25  SO  In. 

Scale  of  Lengths 


Fig.   167. 

With  this  premise  we  shall  give  the  graphic  analysis 
based  upon  the  theorem  of  the  three  moments,  but  we  shall 
not  explain  the  reason  of  the  successive  operations,  referring 
the  reader  to  treaties  on  the  resistance  of  materials.  First 
consider  the  upper  front  spar  (Fig.  167);  Jet  XY  be  its 
length  and  A,  B,  C,  D,  its  supports,  made  by  the  struts. 
Let  each  span  be  divided  into  three  equal  parts  by  means 
of  trisecting  lines  aai,  bbi,  cci,  etc.  For  each  support  with 
the  exception  of  the  first  and  last  ones,  the  difference  be- 
tween the  third  parts  of  its  adjacent  spans  shall  be  deter- 
mined; and  that  difference  is  layed  off  starting  from  the 
support,  toward  the  bigger  span.  In  our  case  we  subtract 
the  third  part  of  span  BC  from  the  third  part  of  span  AB, 


MAIN  PLANES  AND  CONTROL  SURFACES  281 

and  the  difference  is  layed  off  starting  from  B  toward  A. 
Thus  V  is  obtained.  The  line  mini  drawn  through  V  per- 
pendicular to  XY  is  called  counter  vertical  of  support. 
Analogously  one-third  of  BC  is  subtracted  from  one-third 
of  CD,  and  its  difference  is  laid  off  from  C  toward  D,  fixing 
a  second  counter  vertical  of  support  nrii. 

Starting  from  A  (Fig.  167)  let  us  draw  any  straight  line 
that  will  cut  the  trisecant  hbi,  and  the  first  counter  vertical 
of  support  mmi  in  the  points  E  and  F  respectively. 

Draw  the  straight  Une  EB  which  prolonged  will  cut  the 
first  trisecant  of  the  second  span  cci  in  the  point  G.  Join 
G  with  F  by  a  straight  line  which  will  cut  XF  at  the  point 
H.  This  point  is  called  the  right-hand  point  of  support  B. 
Starting  from  H  we  draw  any  straight  line  that  will  meet 
the  second  trisecant  of  the  second  span  ddi  and  the  second 
diagonal  nui  at  the  points  M  and  A^  respectively.  Find 
the  point  P  by  prolonging  the  straight  line  between  M  and 
C.  Point  0,  the  right-hand  point  of  the  second  support, 
is  given  by  the  intersection  of  line  AT  and  hue  XY.  In 
order  to  find  the  left-hand  points  for  the  supports  C  and 
B,  draw  the  straight  hne  PD  which  will  interest  the  counter 
vertical  nui  at  point  Q.  Point  R  where  the  lines  MQ  and 
XY  intersect  each  other  will  be  the  left-hand  point  of 
support  C.  Starting  from  R  draw  the  line  RG  which  will 
cut  the  first  counter  diagonal  at  point  S.  Point  T,  the 
point  of  intersection  of  hues  SE  and  XY  will  be  the  left- 
hand  point  of  support  B. 

The  right-hand  and  left-hand  points  being  known,  we 
shall  suppose  that  we  load  one  span  at  a  time,  determining 
the  bending  moments  which  this  load  produces  on  all  the 
supports.  Summing  up  at  every  support  the  moments  due 
to  the  separate  loads,  we  shall  obtain  the  moments  origin- 
ated by  the  whole  load. 

The  moment  on  the  external  supports  is  equal  to  that 
given  by  the  load  on  the  cantilever  ends,  as  it  cannot  be 
influenced  by  the  loads  on  the  other  spans,  owing  to  the 
fact  that  the  cantilever  beam  can  rotate  around  its  support. 
The  load  on  the  cantilever  spans  however  affects  the  other 


282 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


spans.     To  determine  this  effect  we  proceed  in  the  follow- 
ing manner:  Consider  support  A   (Fig.  168);  the  moment 

wl- 
at  this  support  is  equal  to   ^>  calling  w  the  load  in  lb.  per 

linear  inch  and  I  the  length  of  the  span  in  inches.     Lay  off, 

to  any  scale,  the  segment  A  A'  =   ^   * 

Let  us  then  draw  the  straight  line  A'T;  it  will  intersect 
the  vertical  line  through  support  B  at  point  1 ;  the  segment 
IB  measures,  to  the  scale  of  moments,  the  moment  that  the 
load   on   the   cantilevered   span   produces   on   support   B. 


Scale  of  Uengtha. 


Scale  of  Moments. 


Fig.  168. 


Then  draw  the  straight  line  122;  it  will  meet  the  vertical  line 
through  support  C  at  T;  the  segment  I'C  measures,  always 
to  the  scale  of  moments,  the  moment  originated  on  support 
C  by  the  load  of  the  cantilevered  span.  The  moment  in  D 
cannot  be  influenced  by  the  cantilever  load  on  X  ^. 

Let  us  now  determine  the  effect  of  the  load  on  span  AB, 
on  the  moment  of  the  various  supports.  Draw  FG  perpen- 
dicular bisectrix  oi  AB  and  lay  off,  to  the  scale  of  moments, 

w  "X.  l^ 
a  segment  FG  equal  to  — ^ — ;  that  is,  equal  to  the  moment 

which  would  be  obtained  at  the  center  point  of  AB,  by  a, 
unit  load  w,  if  AB  were  a  free-end  span  supported  at  the 
extremities.     From  T,  the  left-hand  point  of  support  B, 


MAIX  PLANES  AXD  CONTROL  SURFACES  283 

raise  a  perpendicular  which  cuts  line  GB  at  W.  Draw 
line  AW  to  meet  the  perpendicular  through  support  T  at 
point  2.  The  segment  B2  read  to  scale,  will  give  the  mo- 
ment on  support  B  due  to  the  load  on  AB. 

Point  2'  is  obtained  by  prolonging  line  2R  until  it  meets 
the  perpendicular  through  C  at  2'.  Segment  C-2'  represents 
to  the  scale  of  moments,  the  moment  on  support  C  due  to 
the  load  on  AB. 

In  order  to  find  the  effect  of  the  load  of  span  BC  on  the 
other  spans,  proceed  analogously;  that  is  lay  off  ML  on  the 

bisectrix  of  BC,  equal  to  scale,  to  the  moment  ML  =  ^^' 

8 

Let  us  find  points  N  and  P  as  indicated  in  the  figure  and 
let  us  draw  the  line  NP  which  prolonged  will  meet  the  per- 
pendiculars on  supports  B  and  C  at  points  3  and  3'.  Seg- 
ments 5-3  and  C-3'  read  to  the  scale  of  moments,  will  give 
the  moments  produced  by  the  load  of  span  BC  on  the  sup- 
ports B  and  C  respectively. 

Proceeding  as  for  spans  XA  and  AB  we  obtain  the 
moments  originated  on  BC  by  the  loads  on  spans  CB  and 
BY.     The  construction  is  clearly  indicated  in  Fig.  168. 

Resuming,  we  shall  have  the  moment  originated  by  canti- 
lever loads  on  the  supports  A  and  D,  and  the  moment 
originated  by  the  loads  on  all  the  different  spans,  on  the 
supports  B  and  C. 

For  the  point  of  support  B  the  moment  due  to  the  canti- 
lever load  is  equal,  read  to  the  scale  of  moments,  to  dis- 
tance B-1,  the  moment  due  to  the  load  on  AB  is  equal  to 
B-2,  the  moment  due  to  the  load  on  BC  is  equal  to  B-3, 
the  moment  due  to  the  load  on  CD  is  equal  to  B-4'  and 
that  due  to  the  cantilever  load  on  Z)F  is  equal  to  B-5'.  If 
we  assume  that  the  distances  above  the  axis  XY  are  positive 
and  those  below  are  negative,  the  total  moment  BB'  on 
support  B  will  be  equal  to  the  algebraic  sum  of  the  moments 
B-1,  B-2,  B-3,  B-4:',  and  B-5'. 

Analogously  the  algebraic  sum  CC  will  represent  the 
total  moment  on  C.  The  total  moment  on  the  external 
supports  will  naturally  remain  the  one  due  to  cantilevers, 


284 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


and  consequently  equal  to  A  A'  and  DD'.  In  order  to  find 
the  variations  of  the  bending  moment  on  all  the  spans,  the 
load  being  uniformly  distributed,  we  must  draw  the  para- 
bolse  of  the  bending  moments  as  though  the  spans  were 
simply  supported  (Fig.  169). 


Scale  of  Moments 


Fig.   169. 


Fig.   170. 


Then  the  difTerence  between  the  ordinates  of  the  parabolas 
and  those  of  the  diagram  AA'  B'  C  D'  D  give  us  the  diagram 
XA'a'  B'  y  C  c'  D'  YX  which  represents  the  diagram  of 
the  bending  moment  (Fig.  169). 

Knowing  the  diagram  of  the  bending  moments,  it  is  easy 


MAIN  PLANES  AND  CONTROL  SURFACES 


285 


through  a  process  of  derivation  applying  the  common 
methods  of  graphic  statics,  to  find  the  diagram  of  the 
shearing  stresses,  and  consequently  the  reactions  on  the 
supports  (Fig.  170).  The  scale  of  forces  is  obtained  by 
multiplying  the  basis  H  of  the  derivation,  by  the  ratio 
between  the  scale  of  moments  and  that  of  the  lengths.  In 
Fig.  170  the  scale  of  forces  has  been  drawn,  and  on  the 
supports  the  corresponding  numerical  values  of  the 
reactions  have  been  marken. 

Furthermore,  from  the  diagram  of  bending  moments  we 
can  obtain  the  elastic  curve,  which  will  be  needed  later. 


0  25  50Irv 

Scale  ot  Liinyths 


8000        16000  in 
Scale  ot  Moments 


Fig.   171. 


)  15.0        3a01nn(^ 

Scale  at  Deflections 


In  fact,  let  us  remember  that  the  analytic  expression  of 
the  bending  moment  is  given  by 


Ms   =  E  X  I  X 


and  consequently 


y 


rifd-f 


M„  dx' 


that  is,  by  double  integration  of  the  diagram  of  M^  we 
obtain  the  deflections  y,  that  is,  we  obtain  the  form  which 
the  neutral  axis  of  the  spar  assumes,  and  which  is  called 
elastic  curve  (Fig.  171). 

We  shall  not  pause  in  the  process  of  graphic  integration, 
as  it  can  be  found  in  treaties  on  graphic  statics. 


286 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


We  shall  make  use  of  the  elastic  curve  for  the  determina- 
tion of  the  supplementary  moments  produced  on  the  spars 
by  the  compression  component  of  the  vertical  and  hori- 
zontal trussings. 


40  In. 
5cale   of  Lengths 


Fig.   172. 


Figs.  167,  168,  169,  170  and  171  refer  to  the  calculation 
of  the  upper  front  spar.  In  Figs.  172,  173,  174,  175  and 
176  instead,  the  graphic  analysis  of  the  lower  front  spar  is 
developed. 


0  20        40  li 

Scale  of  Length; 


Fig.   173. 


On  these  figures,  beside  the  unit  loads  which  are  already 
known,  the  scale  of  the  moments,  of  the  lengths  and  of  the 
forces  are  also  indicated. 

The  preceding  diagrams  also  give  the  bending  moments. 


MAIN  PLANES  AND  CONTROL  SURFACES  287 


0  12  I421nji(0) 

6cal6  of  Oeflec+iona 


FiQ.  176. 


288  AIRPLANE  DESIGN  AND  CONSTRUCTION 

the  shearing  stresses  and  the  reactions  on  the  supports  for 
the  rear  spars;  in  fact  it  suffices  to  multipl}^  both  the  values 
of  the  forces  and  those  of  the  moments  by  0.92,  as  the  spans 
are  the  same,  and  the  loads  per  hnear  inch  of  the  rear 
spars  are  equal  to  0.92  of  the  loads  of  the  front  spars. 

A  special  note  should  be  made  of  the  scales  of  ordinates 
for  the  elastic  curve;  these  are  inversely  proportional  to 
the  product  E  X  I,  the  elastic  modulus  by  the  moment  of 
inertia,  and  consequently  they  vary  from  spar  to  spar. 
But  we  shall  return  to  this  in  speaking  of  the  unit  stresses 
in  spars. 

(5)  Knowing  the  reactions  upon  the  supports,  it  is  possi- 
ble to  calculate  the  vertical  trussings.  Since  the  front 
trussing  has  the  same  dimensions  as  the  rear  one,  and  since 
the  reactions  on  the  supports  are  in  the  ratio  0.92,  it  suffices 
to  calculate  only  the  first. 


Upper  Spar Upper  Spar 


Fig.    177. 

The  vertical  trussing  is  composed  of  two  spars,  one  above, 
and  the  other  below,  connected  by  struts  capable  of  resist- 
ing compression,  by  bracings  called  diagonals,  which  must 
resist  tension,  and  by  bracings  called  counter  diagonals 
which  serve  to  stiffen  the  structure  (Fig.  177).  In  flight, 
the  counter  diagonals  relax  and  consequently  do  not  work; 
for  the  purpose  of  calculation  we  can  consequently  con- 
sider the  vertical  trussing  as  though  it  were  made  only  of 
spars,  struts,  and  diagonals;  furthermore,  because  of  the 
symmetry  of  the  machine,  for  simplicity  we  shall  consider 
only  one-half  of  it,  as  evidently  the  stresses  are  also  sym- 
metrical (Fig.  178);  the  plane  of  symmetry  will  naturally 
have  to  be  considered  as  a  plane  of  perfect  fixedness. 

With  that  premise  let  us  remember  that  for  equilibrium 
it  is  first  of  all  necessary  that  the  resultant  of  the  external 


MAIN  PLANES  AND  CONTROL  SURFACES 


289 


forces  be  equal  to  zero.  The  reactions  upon  the  supports 
are  all  vertical  and  directed  from  bottom  to  top ;  their  sum 
is  equal  to  5695  lb.;  now,  this  force  is  balanced  by  that 
part  of  the  weight  of  the  machine  which  is  supported  at 
point  A  and  which  is  exactly  equal  to  5695  lb.  Moreover 
it  is  necessary  that  in  any  case  the  appHed  external  force 
(reaction  at  support),  be  in  equilibrium  with  the  internal 
reaction;  that  is,  as  it  is  usually  expressed  in  graphic  statics, 
it  is  essential  that  the  polygon  of  the  external  forces  and  of 


Fig.   178. 


the  internal  reactions  close  on  itself.  This  consideration 
enables  the  determination  of  the  various  internal  reactions 
through  the  construction  of  the  stress  diagram,  illustrated, 
for  our  example,  in  Fig.  179. 

Referring  to  treaties  on  graphic  statics  for  the  demonstra- 
tion of  the  method,  we  shall  here  illustrate,  for  convenience, 
the  various  graphic  operations. 

The  values  of  the  reactions  on  the  supports  individuated 
by  zones  ab,  be,  cd,  and  de  are  laid  off  to  a  given  scale  on 
AB,  BC,  CD,  and  DE  (Fig.  179);  from  B  and  C  we  draw 
two  parallels  to  the  truss  members  determined  bj^  the 
zones  bh  and  ch  respectively;  in  BH  we  shall  have  the 


290 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


0  1000        2000  lbs. 

Scale  •of  Forces 


FiQ.  179. 


MAIN  PLANES  AND  CONTROL  SURFACES 

/44  29  In 


291 


0  500  100  lbs. 

Scale  of  Forces 

Fig.  180. 


292  AIRPLANE  DESIGN  AND  CONSTRUCTION 

stress  corresponding  to  member  bh,  and  in  CH  that  corre- 
sponding to  the  member  ch.  From  points  H  and  D  we 
draw  the  parallels  to  the  members  gh  and  gd;  in  HG  and  DG 
we  shall  have  the  stresses  in  hg  and  dg ;  from  points  E  and  G 
we  draw  the  parallels  to  the  members  determined  by  zones 
ef  and  gf;  in  EF  and  GF  we  shall  obtain  the  stresses  in 
these  members;  finally  from  points  G  and  A  we  draw  the 
parallels  to  the  members  individuated  by  zones  gi  and  at, 
obtaining  the  corresponding  stresses  in  GI  and  AI.  The 
arrows  of  the  stress  diagram  enable  the  easy  determination 
of  which  parts  of  the  truss  are  subjected  to  tension  and 
which  to  compression. 

In  Fig.  179,  beside  marking  the  scales  of  lengths 
and  of  forces,  we  have  marked  the  lengths  and  the 
stresses  corresponding  to  the  various  parts,  adopting  + 
signs  for  tension  stresses,  and  —  signs  for  compression 
stresses.  By  multiplying  these  stresses  by  0.92  we  shall 
obtain  the  values  of  the  stresses  of  the  rear  trussing. 

The  counter  diagonals  which  do  not  work  in  normal 
flight,  function  only  in  case  of  flying  with  the  airplane 
upside  down.  For  this  case,  which  is  absolutely  excep- 
tional, a  resistance  equal  to  half  of  that  which  is  had  in 
normal  flight  is  generally  admitted.  The  determination  of 
stresses  is  analogous  to  that  made  for  normal  flight  and  is 
shown  in  Fig.  180. 

Based  upon  the  values  found  in  the  preceding  construc- 
tion. Table  34  can  be  compiled.  That  table  permits  the 
calculation  of  the  bracings  and  struts. 

The  calculation  of  the  bracings  presents  no  difficulties; 
it  is  sufficient  to  choose  cables  or  wires  having  a  breaking 
strength  equal  to  or  greater  than  that  indicated  in  the  table; 
naturally  the  turnbuckles  and  attachments  must  have  a 
corresponding  resistance.  Table  35  gives  the  dimensions 
of  the  cables  selected  for  our  example.  For  the  principal 
bracings  we  have  adopted  double  cables,  as  is  generally 
done  in  order  to  obtain  a  better  penetration;  in  fact  not 
only  does  the  diameter  of  the  cable  exposed  to  the  wind 


MAIN  PLANES  AND  CONTROL  SURFACES 


293 


Table  34 


Front  vertical  truss 

Rear  vertical  truss 

Normal  position 

Inverted  position 

Normal 

1 

position 

Inverted  position 

Member 

1 

Tension 

Com- 
pression 

Tension 

Com- 
pression 

!  Tension 

1 

1 

Com- 
pression 

Tension 

Com- 
pression 

A-B 

6120 

130 

4710 

120 

B-E 

1400 

.... 

2800 

1290 

2580 

F-C 

5200 

620 

4780 

570 

A-C 

6380 

6870 

D-C 

200 

2330 

180 

2140 

A-D 

1500 

990 

1380 

910 

B-B' 

5780 

3750 

6320 

3450 

C-C 

7600 

2650 

6990 

2440 

B-D 

2800 

2580 

Table  35 


Member 

Stress 
coef.lO 

Number 

of  cables 

used 

Diameter 

of  cable, 

in. 

Ultimate 

strength 

of  cable, 

lb. 

Total 
ultimate 
strength. 

Coef. 

of 
safety 

£ 

A-C 

-f6380 

2 

He 

4200 

8400 

13.1 

I 

B-D 

-f2800 

1 

H 

2000 

2000 

7.1 

■g 

B-E 

-h4700 

1 

%2 

2800 

2800 

5.9 

£ 

C-F 

+9200 

1 

%2 

5600 

5600 

6.1 

g 

A-C 

+5870 

2 

Ke 

4200 

8400 

14.3 

2 

B-D 

+2580 

1 

H 

2000 

2000 

7.7 

» 

B-E 

+4320 

1 

H2 

2800 

2800 

6.5 

(S 

C-F 

+8500 

1 

%2 

5600 

5600 

6.6 

294  AIRPLANE  DESIGN  AND  CONSTRUCTION 

result  smaller,  but  it  becomes  possible  to  streamline  the 
two  cables  by  means  of  wooden  faring. 

For  the  struts,  which  can  be  considered  as  solids  under 
compression,  it  is  necessary  to  apply  Euler's  formula  which 
gives  the  maximum  load  W  that  a  solid  of  length  I  with  a 
section  having  a  moment  of  inertia  /  can  support 

In  that  formula  a  is  a  numerical  coefficient  and  E  is  the 
elastic  modulus  of  the  material  of  which  the  solid  is  made. 

The  theory  gives  the  value  10  for  coefficient  a.  We 
shall  quickly  see  that  practically  it  will  be  convenient  to 
adopt  a  smaller  coefficient  in  consideration  of  practical 
unforeseen  factors. 

Let  us  remember  that  the  struts,  being  exposed  to  the 
wind,  present  a  head  resistance  which  must  be  reduced  to  a 
minimum  by  giving  them  a  shape  of  good  penetration  as 
well  as  by  reducing  their  dimensions  to  the  minimum. 
This  last  consideration  shows,  by  what  has  been  said  in 
Chapter  XVI,  that  for  struts  it  is  convenient  to  use  mate- 
rials which  even  having  high  coefficients  Ai  and  Ai  have  a 
high  specific  weight. 

Then  the  best  material  for  struts  is  steel.  In  Chapter 
XVI  a  table  has  been  given  of  oval  tubes  normally  used 
for  struts,  with  the  most  important  characteristics,  such  as 
weight  per  unit  of  length,  area  of  section,  relative  moment 
of  inertia,  etc. 

Let  us  apply  Euler's  formula  to  these  tubes,  remembering 
that  for  them  I  =  td^,  where  t  is  the  thickness  and  d  is  the 
smaller  axis.     We  shall  have 

W   =   ay 

Remembering  then  that  the  area  of  these  struts  is  given 
with  sufficient  approximation  by  the  expression  A  = 
Q.^ltd  the  preceding  formula  can  be  written  as  follows 

TT  _  a  XE  1 

A  ~    6.37    ^  /IV 


(i) 


MAIN  PLANES  AND  CONTROL  SURFACES 


295 


where 

W 

—r  =  unit  stress  of  the  material 
A 


=  ratio   between   that   portion  of  the  length  which  can 


be  considered  as  free  ended,  and  the  minimum  dimension  of 
the  strut. 


IIXIU 

10 

9 

8 

I 

\ 

«=47.,0%(!). 

A     7 

\ 

\ 

\ 

\ 

'^;^ 

4 

^^ 

i 

\ 

3 

~ 

-^  . 

4^^. 

/• 

\ 

•^^ 

'/ 

\ 

2 

».^ 

\ 

^V. 

^ 

^ 



/-» 

0        10      20      30      40       50      60       TO      80      90      100 
I  _ 
d 
Fig.   181. 


Adopting  pounds  and  inches  as  the  unit,  we  have  E  = 
3  X  10^  and  consequently 

W  1 

^  =  47  X  10^  X  a  X  jiy, 


(f 


290  AIRPLANE  DESIGN  AND  CONSTRUCTION 

Naturally  this  formula  can  be  applied  only  for  high  values 

of  the  ratio    ,;   practically  below  the  value    ,  =  60  this 

formula  can  no  longer  be  relied  upon.  In  Fig.  181  the 
diagram  corresponding  to  the  preceding  formula  is 
given,  drawing  the  diagram  with  a  dotted  instead  of  a 

full  line  for  the  values  of  -^  <  60.     For  those  values  the 

practical  diagram  is  shown  by  a  dot  and  dash  line. 

In  Tables  36  to  39  we  have  tabulated  the  results  of  some 
of  the  many  tests  on  metal  struts  which  have  been  made 
at  our  works.  In  these  tables  the  practical  value  of  coeffi- 
cient a  of  Euler's  formula  has  been  calculated;  it  is  seen 
that  while  in  some  tests  a  has  a  value  higher  than  10, 
in  general  it  gives  lower  values.  That  depends  ujoon  some 
struts  being  manufactured  by  hand  and  some  being  rolled, 
and  also  upon  the  thickness  of  the  sheet  and  the  dimensions 
of  the  sections  being  not  always  uniform.  Based  on  aver- 
age values  we  can  therefore  assume  that  for  properly  manu- 
factured struts  a  coefficient  a  =  8  can  be  adopted  for 
computation  purposes. 

With  this  premise  it  is  simple,  when  the  ultimate  stress 
which  a  strut  must  withstand,  and  its  length,  are  known, 
to  determine  its  dimensions. 

Moreover  infinite  solutions  exist,  since  formula  (1)  when 
W  and  I  are  given,  can  be  satisfied  by  infinite  couples  of 
values  A  and  d. 

Evidently  by  increasing  d,  the  value  of  A  becomes 
smaller  and  consequently  the  weight  of  the  strut  diminishes; 
from  that  point  of  view  it  would  be  convenient  to  use  struts 
having  large  dimensions  and  small  thicknesses.  However, 
the  increase  of  d  increases  the  head  resistance  of  the  airplane, 
and  increases  the  power  necessary  to  fly. 

Therefore  it  becomes  necessary  to  adopt  that  solution 
which  requires  the  minimum  expension  of  power. 

If  /3  is  the  weight  per  horsepower  lifted  by  the  airplane, 
y  is  the  weight  of  one  foot  of  strut  of  width  d,  k  its  coeffi- 
cient of  head  resistance  as  was  definitely  stated  in  Chapter 


MAIN  PLANES  AND  CONTROL  SURFACES 


297 


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298 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


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MAIN  PLANES  AND  CONTROL  SURFACES 


299 


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300 


AIRPLANE  DESIGN  AND  CONSTRUCriON 


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MAIN  PLANES  AND  CONTROL  SURFACES  301 

VII,  V  the  speed  of  the  airplane  in  m.p.h.,  and  p  the  propeller 
efficiency,  the  total  power  p  absorbed  by  a  foot  of  strut 
will  be  equal  to 

p  =  ^  +  -  X  267  X  10-9  k^V' 

Now  the  weight  y  is  equal  to 

7  =  12  X  A  X  0.280  lb.  =  3.36A  lb. 
where  A  is  expressed  in  square  inches. 

In  Chapter  III  we  have  seen  that  k  =  3.5  for  struts  of  the 
type  which  we  are  studying.  Then,  taking  an  average 
value  p  =  0.75  we  shall  have 

p  =  ?^y^  +  103.6  X  10-9  ^ys 

Formula  (1)  permits  expressing  A  as  function  of  d 
W 
^       47  X  10^  X  a  ^ 
consequently  we  shall  have 

Supposing  W,  I,  a,  jS  and  V  to  be  known,  the  preceding 
equation  gives  the  expression  of  total  power  (that  is,  the 
resultant  of  the  weight  and  head  resistance),  absorbed  by 
one  foot  of  strut  as  function  of  the  minor  axis  d  of  its  section. 

Evidently  the  designer's  interest  is  to  find  the  value  of  d 
that  makes  p  minimum;  but  that  value  is  the  one  which 
makes  the  derivative  of  the  second  term  of  the  preceding 
equation  equal  to  zero,  that  is,  the  one  which  satisfies 
the  equation 

-2  x'-^'^^V  103.6X10- 7-0 
from  which 

wxr- 


©' 


13.8  X 


Let  us  remember  that  the  symbols  have  the  following 
significance : 
W  =  maximum  braking  load  which  a  strut  must  support, 
I  =  length  of  strut, 


302  AIRPLANE  DESIGN  AND  CONSTRUCTION 

a  =  coefficient  of  Euler's  formula, 

jS  =  ratio  between  the  total  weight  and  power  of  the 
airplane, 

V  =  speed  of  the  airplane, 

For  our  example  the  weight  of  the  airplane  is  2130  lb. 
and  its  power  is  300  H.P.;  then  /3  =  7.1 ;  the  foreseen  speed 
is  about  158  m.p.h.  Furthermore  for  a  we  can  adopt  the 
value  8. 

Then  the  preceding  formula  becomes: 

d'  =  61.5  X  10-9  WP  (2) 

Euler's  formula,  for  a  =8,  gives 

5  =  3.76  X  10-'  X  -y]^,  (3) 

(^) 

Equations  (2)  and  (3)  enable  obtaining  d  and  A,  when  W 
and  I  are  known;  then  since 

A  =  6.37^ 
the  thickness  t  of  the  tube  is  easily  obtained. 

The  computations  of  the  struts  for  the  airplane  in  our 
example,  Table  40,  have  been  made  with  these  criterions. 

Before  passing  to  the  calculation  of  the  horizontal  truss- 
ings  it  is  necessary  to  mention  the  vertical  transversal  truss- 
ings  which  serve  to  unite  the  front  and  rear  struts  (Fig.  182). 
The  scope  of  these  bracings  is  that  of  stiffening  the  wing 
truss  and  at  the  same  time  of  establishing  a  connection 
between  the  diagonals  of  the  principal  vertical  trussings. 
Their  calculation  is  usually  made  by  admitting  that  they 
can  absorb  from  ^  to  %  of  the  load  on  the  struts. 

(c)  The  horizontal  trussings  have  the  scope  of  balancing 
the  horizontal  components  of  the  air  reaction.  As  we  have 
seen,  it  is  sufficient  for  the  calculation,  to  assume  for  these 
horizontal  components  25  per  cent,  of  the  value  of  the 
vertical  reactions. 

As  an  effect  of  the  stresses  in  the  vertical  trussings, 
a  certain  compression  in  the  spars  of  the  upper  wings 
and  a  certain  tension  in  the  spars  of  the  lower  wings  are 
developed. 


MAIN  PLANES  AND  CONTROL  SURFACES 


303 


As  an  effect  of  the  stresses  in  the  horizontal  trussings  we 
have  a  certain  tension  in  the  front  spars  and  a  certain  com- 
pression in  the  rear  spars. 


Table  40 


Member 

Stress 
coef.  10 

r/, 
lb. 

Length 
in. 

Diameter 
d 
(theo- 
retical), 
in. 

Thickness 
t 
(theo- 
retical), 
in. 

Diameter 

d 

(actual), 

in. 

Thickness 

t 

(actual), 

in. 

II 

I 

11 
III 

-1500 
-2800 
-5200 

65 
20 
20 

1 

0.731    1    0.068 
0.883        0.068 
1.085        0.068 

0.788 
0.983 
1.180 

0.065 
0.065 
0.065 

si 

1 

11 
111 

-1380 
-2580 
-4780 

65 
20 
20 

0.710        0.068 
0.860        0.068 
1.057        0.066 

0.788 
0.983 
1.180 

0.065 
0.065 
0.065 

Fig.  182. 


Consequently  in  the  various  spars  there  is  a  distribution 
of  stresses  as  shown  in  Table  41. 


304  AIRPLANE  DESIGN  AND  CONSTRUCTION 

Table  41 


Upper  front 
Upper  rear 
Lower  front 
Lower  rear 


Effect  of  vertical  trussing 


Compression 
Compression 
Tension 
Tension 


Effect  of   horizontal    tr 


Tension 
Compression 
Tension 
Compression 


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MAIN  PLANES  AND  CONTROL  SURFACES 


305 


We  see  then  that  while  there  is  partial  compensation  of 
stresses  in  the  upper-front  and  lower-rear  spars,  in  the  other 
two  spars  instead  the  stresses  add  to  each  other.  The 
spar  which  is  in  the  worst  condition  is  the  upper-rear  one, 


&cale  of  Forces 


STRESS   DIAGRAM 


Fig.  185. 


which  is  doubly  compressed.  In  order  to  take  the  stress 
from  it,  at  least  partially,  it  is  practical  to  adopt  drag  cables 
which  anchor  the  wings  horizontally.  Usually  these  drag 
cables  anchor  the  upper  wings  only.  Sometimes  also  the 
lower  ones. 


306  AIRPLANE  DESIGN  AND  CONSTRUCTION 

111  Fig.  183  the  schemes  of  the  horizontal  trussings  for 
the  lower  and  upper  wing  are  given.  They  are  made  of 
spars,  a  certain  number  of  horizontal  transversal  struts, 
and  of  steel  wire  cross  bracing.  As  we  have  already  seen, 
in  Fig.  183  the  acting  forces  have  been  indicated  equal  to 
25  per  cent,  of  the  vertical  components.  In  Figs.  184  and 
185  the  graphic  analysis  of  the  horizontal  trussings  of  the 
lower  and  upper  wings  have  been  given;  as  they  are  en- 
tirely analogous  to  those  described  for  the  vertical  truss- 
ing, we  need  not  discuss  them. 

{d)  Analysis  of  the  Unit  Stresses  in  the  Spars. — This 
analysis  is  usually  made  following  an  indirect  method,  that 
is,  under  form  of  verification.  Wc  fix  certain  sections  for 
the  spars  and  determine  the  vmit  load  corresponding  to  the 
ultimate  load  of  the  airplane. 

After  various  attempts,  the  most  convenient  section  is 
determined. 

Let  us  suppose  that  in  our  case  the  sections  be  those  indi- 
cated in  Fig.  186. 

The  areas  and  the  moment  of  inertia  are  determined  first. 
The  areas  are  determined  either  by  the  planimeter  or  by 
drawing  the  section  on  cross-section  paper.  The  moment 
of  inertia  is  determined  either  by  mathematical  calculation 
or  graphically  by  the  methods  illustrated  in  graphic  statics. 
Fig.  187  gives  this  graphic  construction  for  the  upper  rear 
spar. 

Practically  two  principal  methods  of  verification  are  used : 

A.  The  elastic  curve  method. 

B.  The  Johnson's  formula  method. 

A.  This  method  consists  of  determining  the  total  unit 

stress  /r  by  adding  the  three  following  stresses : 

p 

1.  Stresses  of   tension  or  of   pure   compression  fc  =-r 

where  P^  is  the  sum  of  the  stresses  Pl  and  P^  originated  in 
the  considered  part  of  the  spar  by  vertical  and  horizontal 
load,  and  A  is  the  area  of  the  section. 

M 

2.  Stress  due  to  bending  moments /j,/=  -^  where  M  is  the 


MAIN  PLANES  AND  CONTROL  SURFACES 


307 


308 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


'■JI90  0 


'•lOOZ 


MAIN  PLANES  AND  CONTROL  SURFACES  309 

bending  moment  and  Z  is  the  section  modulus.  We  shall 
remember  that  this  modulus  is  obtained  by  dividing  the 
moment  of  inertia  I  by  the  distance  of  the  farthest  fiber 
from  the  neutral  axis. 

P     X  A 

3.  Bending  stress  due  to  the  compression  stress  f^  =  — 

A 
where  P^  is  the  compression  stress  and  A  is  the  maximum 
deflexion  of  the  span  which  is  obtained  from  the  elastic 
curve.  In  order  to  know  A  it  is  necessary  to  know  the 
elastic  modulus  E  of  the  material  because  this  modulus 
enters  into  the  equation  which  gives  the  scale  of  the  elastic 
curve  (see  Figs.  171  and  176). 

By  adding  the  values /c,  j^j  and/^  we  obtain /r,  which  is 
the  total  unit  stress,  in  our  case  corresponding  to  a  load 
equal  to  ten  times  the  normal  flying  load.  If  we  wish  to 
determine  the  factor  of  safety  of  the  section  it  is  necessary 
to  know  the  modulus  of  rupture  of  the  material ;  this  modu- 
lus of  rupture  divided  by  Y^^^  Jt  gives  the  factor  of  safety. 

We  have  given  in  Chapter  XVI  the  moduli  of  rupture 
to  bending  for  various  kinds  of  wood.  For  combined  stresses 
of  bending  and  compression  stresses,  it  is  necessary  to  adopt 
an  intermediate  modulus  of  rupture.  Fig.  188  shows  dia- 
grams giving  the  modulus  of  rupture  as  function  of  ratio 

^  for  the  four  following  kinds  of  wood;  Douglas  fir,  port- 

orford,  spruce  and  poplar. 

In  Table  42  all  the  preceding  data  for  the  sections  of  the 
spars  most  stressed  has  been  collected.     In  this  table 
Fi^  =  stress  due  to  vertical  trussings. 
Pj)  =  stress  due  to  horizontal  trussings. 
Py  =  Pi,  +  P^  =  total  stress  due  to  both  trussings. 
For  these  stresses  the  —  sign  has  been  adopted  when  they 
are  compression  stresses  and  the  -|-  sign  when  they  are  ten- 
sion stresses. 

A  =  area  of  the  section. 

Jc  ^ 

E  =  elastic  modulus  of  the  material. 


310 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


o         o        o        O         O         o 
o        o       o       9        o        o 


MAIN  PLANES  AND  CONTROL  SURFACES  311 

I  =  moment  of  inertia  of  the  section. 

Z  =  section  modulus. 

M  =  bending  moment  due  to  air  pressure. 

M      . 
Jm^'Y  unit  stress  due  to  this  bending  moment. 

A  =  maximum  deflexion  of  the  span. 
Pr  =  moment  due  to  compression  stress  P^. 

TO         V     A 

/^  =  —^--. =  unit  stress    due  to  the  moment 

originated  by  the  compression  stress. 
S  =  total  shearing  stress. 

s  =  -r  =  unit  stress  to  shearing. 
A. 

fc/fr  =  ratio  between  the  compression  stress  and 
total  stress.  By  using  the  diagrams  of  Fig. 
188,  this  ratio  enables  us  to  determine 
the  modulus  of  rupture,  thence  the  factor 
of  safety. 
B.  The  Johnson's  formula  method  is  based  upon  John- 
son's formula: 

"^      zx(i- 


KEI 

where  I  is  the  length  of  the  span,  i^  is  a  numerical  coefficient 
and  the  other  symbols  are  those  of  the  preceding  method. 

The  value  of  coefficient  K  is  dependent  on  end  conditions 
and  is 

=  10  for  hinged  ends 

=  24  for  one  hinged,  one  fixed 

=  32  for  both  ends  fixed 

In  Table  43  all  the  values  of  the  quantities  necessary 
for  calculating  the  factor  of  safety  by  the  Johnson's  formula 
method  have  been  collected. 

We  see  that  the  factors  of  safety  are  about  equal  to  those 
found  by  the  preceding  method,  with  the  exception  of  that 
corresponding   to   point  B  of  the  upper-rear-spar.     This 


312 


AIRPLAXE  DESIGN  AND  CONSTRUCTION 


Table  42 


PT          -*■ 

f.  =  I'T/A, 

K'    s: 

lb.  per 
sq.  in. 

0  5.70 

0 

-    5120  2.34 

2190 

-    3685} 5.  56 

645 

-   3020  2.34 

1290 

E,  lb. 
per  sq.  in. 


Upper  front 

spar ]   '     C 

D 


0  0 

-5120|  0 

-5120} +1435 
-5780+2850 


1.78X10«   4.02  2.02  20060 


1.78X10'  2.831.84 
1.78X10'  |3.06}2.00 
1.78X10'   2.83  1.84 


65001 
7200  [ 
1210 


Upper    rear 
spar 


. 

0 

0 

014.88 

0 

1.78X10'   2.5l}l.96 

19000 

B 

-4700 

-1435 

-    61352.58 

2380 

1.78X10'   2.10  1.64 

5980 

C 

-4700 

-2865 

-    756514.88 

1550 

1.78X10'  }2.5l}l.96 

6630 

D 

-5320 

-5445 

-11765  2.58 

4370 

1.78X10'    2.101.64 

1          1 

■  1110 

Lower  front  ^ 
spar 


0 
-    200 


-    200  +1110  + 
+  7600  +2220'  + 


05.70 
200  1.98 
910}5.56} 
3820  1.98 

I 


0 

100 

165 

4960 


1.30X10'  i3. 06^2. 00  12220 
1.30X10'  12.52  1.84  7720 
1.30X10'  |3.06  2.00!  7800 
1.30X10'  '2.52  1.84'   5380 


Lower     rear 
spar 


A  \            0             0 

B  -    1851-1110 

C  }-    185-2220 

D  +7000-3600 


129c 
240.^ 


0  1.30X10'    1.92  1.49 

615  I  1.30X10'    1.841.40 

495  1.30X10'  |l.92  1.4!) 

1610  1.30X10'    I.84J1. 40 


11300 
7140 
7270 
4970 


•  No  bolt  holes. 


discrepancy  occurs  because  the  coefficient  K  for  this  point 
should  have  been  32  instead  of  24,  as  was  assumed.  In 
fact,  from  an  examination  of  the  elastic  curve  of  the  upper 
spars  (Fig.  171),  it  is  seen  that  point  A  is  to  be  considered 
as  an  actual  fixed  point,  and  consequently  for  this  point 
the  coefficient  32  should  have  been  taken. 

With  this  single  exception,  the  two  methods  are  practi- 
cally equivalent. 

Before  leaving  the  calculation  of  the  wing  truss,  the  cal- 
culation of  the  shearing  stresses  and  of  the  bending  mo- 
ments which  are  developed  in  the  ribs  should  be  mentioned. 


MAIN  PLANES  AND  CONTROL  SURFACES 


313 


This  calculation,  which  is  usually  made  graphically  is 
illustrated  in  Figs.  189  and  190. 

The  rib  can  be  considered  as  a  small  beam  with  two  sup- 
ports and  3  spans;  the  supports  being  made  by  the  spars. 

Diagram  (a)  of  Fig.  189  gives  the  values  of  the  pressures 


Table  42— (Continued) 

M/Z. 
lb.  per 
sq.  in. 

A, 
in. 

Pr.A. 

in. 
lb. 

j^=Pt.a/Z 

lb.  per 
sq.  in. 

s, 

lb. 

S 

lb.   per 
sq.  in. 

fc=fc+     \ 

in. 2 

Modulus, 
lb.  per 
sq.  in. 

Factor 
safety 

Sec. 

7880 



1040 

185 

7880 

0,000 

9700 

12.3 

n. 

3530 

0.578 

2960 

1600 

900 

385 

7320 

0.299 

8550 

11.6 

I 

3600 

0.578 

2130 

1065 

720 

125 

5310 

0.121 

9250 

17.4 

■ 

660 

0.106 

320 

175 

350 

150 

2125 

0.606 

7450 

35.0 

I 

9700 

950 

195 

9700 

0.000 

9700 

10.0 

■  * 

3640 

0.716 

4390 

2670 

825 

320 

8600 

0.270 

8680 

10.0 

X 

3380 

0.716 

5420 

2840 

660 

135 

7770 

0.197 

8900 

11.5 

f 

680 

0.131 

1540 

940 

320 

125 

5990 

0.723 

7000 

11.7 

6110 
4200 


1030 

180 

6110 

0.000 

7900 

12.9 

1.43 

290 

160 

900 

455 

4460 

0.025 

7850 

17.5 

900 

160 

4065 

0.000 

7900 

19.4 

300 

150 

7890 

0.000 

7900 

10.0 

7600 

955 

195 

7600 

0.000 

7900 

10.4 

■ 

5100 

1.55 

2010 

1435 

830 

395 

7150 

0.086 

7600 

10.6 

I 

4840 

1.55 

3730 

2500 

830 

170 

7835 

0.062 

7800 

10.0 

? 

4350 



280 

130 

5960 

0.000 

7900 

13.2 

along  the  entire  rib;  the  integration  of  this  diagram  gives 
diagram  (6)  of  Fig.  189  whose  ordinates  correspond  to  the 
shearing  stresses. 

In  Fig.  190,  diagram  (o)  represents  diagram  (6)  of  Fig. 
189.  In  order  to  render  this  diagram  more  clearly  it  has 
been  redrawn  in  Fig.  190  (b)  referring  it  to  a  rectilinear 
axis  and  adopting  a  doubled  scale  for  the  shearing  stresses. 

The  integration  of  this  diagram  gives  the  diagram  of  the 
bending  moments.  Fig.  190  (c). 

The  distributions  of  the  shearing  stresses  and  bending 


314 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table 

43 

Member 

Sec. 

PL,  Ib.Pc,  lb. 

Pl^Pd 
lb. 

A, 
sq. 
in. 

l.in. 

^'^    if:.^ 

E, 
lb.  per 
sq.  in. 

J, 
in.« 

A 
B 
C 
D 

0            0 

0  5.70 

0 
2190 
645 
1290 

1 

2    R5 

1. 78X10*4.02 
1.78X10«2.83 
1.78X10' 3.06 
1.78X10' 2.83 

Upper 
front 
spar 

-5120 
-5120 
-5780 

0 
+  1435 
+  2850 

-  5120 

-  3685 

-  3020 

2.34 
5.56 
.3. 

89.76  41.2X10«!l.84  24 
89.76  29.7X10' 2.00  32 
48.18    7. 0X10»  1.84  32 

Upper 
rear 
spar 


A 

oi         0 

B 

-4700|-1435 

C 

-4700j-2865 

D 

-5320-5445 

0  4.88 

■  6135^2.58 

■  756514.88 
■117652.58 


2380  89.76  49.4X10'  1.64 
1550  89.76  61.0X10'  1.96 
4370  48.18  27. 3X10'|1. 64 


1.78X10'  2.51 

1.78X10'2.10 

32  1.78X10'2.51 

32  1.78X10' 2.10 


Lower 
front 
spar 


0  0  05.70 

-  200  0  -      200  1.98 

-  200  +1110  +     910  5.56 
+  7600+2220+   9820:1. 


0  . 

lOOi 

165{ 

,4960  c 

I  I 


2.00  .. 

11. 62X10«ll. 84124 
j 2.00  32 

[1.84132 


1.30X10' 3.061 
1.30X10'  2.52 
1.30X10'|3.06 
1.30X10«i2.52 


Lower 
rear 
spar 


OJ  oj  04.88'        0 1.49.. 

185|-1110|-    1295|2.11'   615j89.96JlO.5X10' I.40I24 
1851-2220  -    240514.88    495,89. 96119. 5X  lO^ll  .49|32 


+  7000  -3600  +    3400  2. 


1.30X10^  1.92' 
1.30X106jl.84 
1.30X10'  1.92 
1.30X10'  1.84 


moments  being  known  the  dimensions  of  the  web  and  of  the 
rib  flanges  can  easily  be  determined. 

In  Fig.  191  a  general  view  of  a  very  light  type  of  rib  is 
given. 

We  shall  now  pass  to  the  calculation  of  the  tail  system 
and  the  control  surfaces.  Figs.  192  and  193  give  respec- 
tively the  assembly  of  the  fin-rudder  group  and  the  sta- 
bilizer-elevator group.  The  calculation  of  their  frame  is 
very  easy  when  the  distribution  of  the  loads  on  the  surface 


MAIN  PLANES  AND  CONTROL  SURFACES 


315 


is  known.     Consequently  only  the  procedure  for  the  cal- 
culation of  these  loads  will  be  indicated. 

Let  us  first  of  all  consider  the  fin-rudder  group  (Fig.  194). 
In  normal  flight  as  well  as  during  any  maneuver  whatever, 
the  distribution  of  the  pressures  on  these  surfaces  is  very 

Table  43 — (Contiriued) 


-l/.in. 
lb. 

KEI 

1- 

pn 

KEI 

M 

s, 

lb. 

-1 

lb. 

per 

sq.in. 

per 
sq.in. 

/^//< 

Mod. 
rupt., 
lb.  per 
sq.  in. 

Factor 
safety 

KEI 

'{^-KEl),\h. 

Sec. 

20660 
6500 
7200 
1210 

7890 

5350 

4330 

690 

1040 
900 
720 
350 

180 
385 
125 
150 

7890 
7540 
4975 
1980 

0.291 
0.130 
0.651 

9700 
8600 
9200 
7300 

12.3 
11.4 

37.0 

■  * 

121.0X106 
174.2X106 
161.0X106 

0.340 
0.170 
0.044 

0.660 
0.830 
0.956 

■ 

I 

19000 

9700 
8130 
5900 
880 

950 
825 
660 
320 

195 
320 
135 
125 

9700 

10510  0.226 
7450  0.203 
5250  0.883 

9700 
8850 
8900 
6600 

10.5 
8.5 
11.9 
12.6 

I 

189.5X106 
143.0X106 
119.3X106 

5980 
6630 
1110 

0.552  0.448 
0.427  0.573 
0.228  0.772 

12220 

6110 
4300 
3900 
2930 

1030 
900 
900 
300 

180 
455 
160 
150 

0110 
4400 
4065 
7890 

0.021 

7900 
7850 
7900 
7900 

12.9 
17.8 
19.4 
10.0 

f 

■ 

T 

78.6X106 

7720  0.021 
7800     

0.979 

5380 

57.4X106'  7140 
80.0X1061  7210 
4970 


0.183J0.817 
0.24410.756 


7600 
6240 
6410 
3550 


955 

195 

7600 

7900 

10.4 

830 

395 

6865  0.090 

7000 

11.0 

830 

170 

6905  0.070 

7G50 

11.1 

280 

130 

5160 

7900 

15.3 

complex  and  varies  according  to  their  profile  and  their 
form. 

Practically,  though,  such  high  factors  of  safety  are  as- 
sumed for  them,  that  it  suffices  to  follow  any  loading  hypo- 
thesis even  if  only  approximate. 

For  instance,  as  it  is  usually  done  in  practice,  the  hypo- 
thesis illustrated  in  the  diagram  of  Fig.  194  (c)  can  be 
adopted.  We  suppose  that  the  unit  load  decreases  linearly 
on  the  fin  as  well  as  on  the  rudder;  in  the  fin  it  decreases 
from  a  maximum  value  u  in  the  front  part  to  a  minimum 


316 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


0  10  20  In 

Scale  of  Lengths 

LOADING   DIAGRAM 


0  A2>  8.6  lb&./lln.In. 

Scale  of  Loads 


TABLE  OF  AREA  WEI6HT5  IN  POUNDS 

Area 

1 

8.2 

3 

4 

5 

6 

7 

8 

9 

10 

II 

12 

13 

14 

15 

16 

IT 

2 

Load 

13.0 

33.5 

33.3 

3T3 

MO 

3Q0 

25.8 

21.6 

18.0 

143 

12.3 

10  1 

83 

6.9 

5.3 

3e 

05 

31B 

Scale  of  Shears 
0              168            336  lbs 
J I 


SHEAR     DIAGRA^M 
Fig.   189. 


MAIN  PLANES  AND  CONTROL  SURFACES 


317 


0  10  20  in 

Scale  of  Lengths 


SHEAR     DIAGRAM  (1) 
J  I  I  I 


0  168         33&  lbs 

Scale  of  Shears 


SHEAR     DIAGRAM  (2) 


0  84  163  lbs. 

Scale  of  Shears. 


MOMENT    DIAGRAM 


0  550         1100  In  lbs 

Scale  of  Moments. 


W 


Fio.  190 


318 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


value  equal  to  0.5  u  in  the  rear 
part.  In  the  rudder  instead, 
the  unit  load  decreases  from  u 
to  zero. 

In  order  to  determine  the 
numerical  value  of  u  the  aver- 
age value  u„  of  the  unit  load  of 
the  surfaces  is  usually  given. 
This  average  value  is  assumed 
so  much  greater,  as  the  airplane 
is  faster;  practically  for  speeds 
between  100  and  200  m.p.h.  we 
can  assume 

u^  =  0.167 

expressing  u^  in  pounds  per 
square  foot. 

In  our  case  we  shall  have 
about  u„,  =  25  lbs.  per  sq.  ft. 
Then  the  surfaces  of  the  fin 
and  rudder  are  divided  into 
sections  (Fig.  194  (a)),  and 
their  areas  are  determined.  In 
our  case  they  are  as  given  in  the 
table  of  Fig.  194  (6);  let  us  call 
a  one  of  these  areas  and  ku 
the  corresponding  unit  load; 
the  load  upon  it  will  be  evi- 
dently aku. 

If  A  is  the  total  area,  we  have 


that  is 


:a  X  k  X  u  =  Au„ 


A    XUr, 


:a  X  k 


The    value    u    having     been 
determined,    we    have    all    the 


MAIN  PLANES  AND  CONTROL  SURFACES 


319 


<m: 


320  AIRPLANE  DESIdX  AND  CONSTRUCTION 


Q 


;l 


U 


-~r 

= — F=— ^ 

\( 

L.  ^ 

^ 

\ 

V 

c 

0 

I 

\\' 

w 

{^ 


V 


MAIN  PLANES  AND  CONTROL  SURFACES  321 


CO 

V/E16HTS 

N 

PO  U  N  DS 

SECTION 

1 

2 

3      4 

5 

6 

7 

8 

e 

10 

II 

12 

13 

14 

lb 

126 

FIN 

4 

Q 

11      13 

1  IS 

18 

18 

20 

Id 



BUDDER 

57 

4e 

38 

24 

13 

2 

b^av 

1 

U  1  > 

Fig.  194. 


ilHrLAXE  DESIGN  AND  CONSTRUCTION 


AREAS 

IN 

SQ. 

FT. 

SECTIONS 

1 

2 

3 

4 

5 

e 

7 

d 

9 

10 

II 

12 

13 

14 

S 

ELEVATOR 

05Z 

073 

OdI 

1.0 

1.06 

08 

0.23 

0.16 

a/0 

0.03 

5.82 

STABILIZa 

0.80 

0.80  1080 

0.19 

061 

055 

0.41 

0.24 

5.06 

TOT/KU 

1088 

LOADING  DIAGRAM 

(c) 


5      6       7       B      S>      lO     ft      12     13      14- 

WEIGHTS     IN    POUNDS 


\'>ECriOHS 

1 

2 

3    U 

S      6 

7 

a     9 

lO 

II 

12 

/3 

14- 

s 

tUEVATORl 

1.8 

95 

211 

3A.5 

46  6  596 

13.7 

95   5.9 

i.d 

204 

{sTASIUZEIi 

77.? 

23.5    25.8 

rj.d 

252 

23.0 

18.2 

11.3 

m 

TOT^L. 

381 

FvG.  106. 


MAIN  PLANES  AND  CONTROL  SURFACES  323 

elementary  values  aku,  which  in  our  case  are  as  given  in  the 
table  of  Fig.  194  (d).  These  loads  being  obtained,  we 
easily  determine: 

(a)  the  center  of  loads  of  the  fin,  that  is,  what  is  usually 
termed  the  center  of  pressure  of  the  fin, 

(6)  the  center  of  loads  or  center  of  pressure  of  the  rudder, 
and 

(c)  the  center  of  loads  of  the  entire  system. 
It  is  then  possible  to  determine  the  reactions  on  the  various 
structures  and  consequently  to  make  the  calculation  of  their 
dimensions,  following  the  usual  methods. 

In  Fig.  195  all  the  operations  previously  described  are 
repeated  for  the  stabilizer-elevator  group,  noting,  however, 
that  for  this  group  we  usually  assume 

u„  =  0.22  X  V 

that  is,  in  our  case  Um  =  35  lbs.  per  sq.  ft. 


CHAPTER  XIX 

STATIC  ANALYSIS  OF  FUSELAGE,  LANDING  GEAR 
AND  PROPELLER 

A.  Analysis  of  Fuselage. — ^Let  us  consider  the  following 
particular  cases: 

(a)  Stresses  in  normal  flight. 

(b)  Stresses  while  maneuvering  the  elevator. 

(c)  Stresses  w^hile  maneuvering  the  rudder. 

(d)  Maximum  stresses  in  flight. 

(e)  Stresses  while  landing. 

(a)  In  normal  flight  the  fuselage  should  be  considered 
as  a  beam  supported  at  the  points  where  the  wdngs  are 
attached  to  it  and  loaded  at  the  various  joints  of  the 
trussing  which  make  the  frame  of  the  fuselage.  In  these 
conditions  it  is  easy  to  determine  the  shearing  stresses  and 
the  bending  moments  when  the  weight  of  the  various  parts 
composing  the  fuselage  or  contained  in  it  are  known. 

Let  us  consider  the  case  of  a  fuselage  made  of  veneer.  As 
w^e  have  seen  in  the  first  part  of  this  book,  such  a  fuselage 
has  a  frame  of  horizontal  longerons  connected  by  wooden 
bracings;  this  frame  is  covered  with  veneer,  glued  and  nailed 
to  the  longerons  and  bracings.  Let  us  suppose  the  frame 
to  be  the  one  shown  in  Fig.  196a. 

First  the  reactions  of  the  various  w^eights  on  the  joints 
of  the  structure,  and  the  reactions  on  the  supports  are 
calculated  (Fig.  1966).  It  is  then  easy  to  draw  the  dia- 
gram of  the  shearing  stresses  (Fig.  196c),  and  of  the  bending 
moments  (Fig.  196d),  corresponding  to  the  case  of  normal 
flight. 

(6)  When  the  pilot  maneuvers  the  elevator,  the  fuselage 
is  subjected  to  an  angular  acceleration,  which  is  easily 
calculated  if  the  moment  of  inertia  of  the  fuselage  is  known. 

324 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


325 


215.7  la 


15.15"  I5J5"  23.10"        24.50"      23.20"    21.80"     2030"   18.30"  n.50"  16.30" IQ.60'\ 

i 

is 

-1 

6   I 

7  :§    ^^   5^^  ,oi  ni  isi 

5         !i         ^         5t       S        S3 

315  In.  ^23IOIn\                                            ISi.lO  In.                                             1 

(") 

1 
> 

II 

§ 

SPACE 

DIAGRAM  . 

-| 

0  30  60  In. 

Scale  of  Lencjths 


Ib^lbs 


SHEAR     DIAGRAM 


0  250  500  lbs 

Scale  of  Shears 


0  5000       10000  Ib&.In 

Scale  of  Momenfa. 


5  6  7         a         9        10 

MOMENT     DIAGRAM 
Fig.   19G. 


326  AIRPLANE  DESIGN  AND  CONSTRUCTION 

In  Fig.  197  the  graphic  determination  of  this  moment  of 
inertia  has  been  made;  its  result  is  /  =  97,000  lb.  X  inch^. 
We  shall  suppose  that  a  force  equal  to  1000  lb.  acts  suddenly 
upon  the  elevator.  Then  remembering  the  equation  of 
mechanics 

do) 


^  =  ^'Xrf* 


where 


C  =  acting  couple 

Ip  =  polar  moment  of  inertia 

-J.   =  angular  acceleration 

and  as  in  our  case 

C  =  1000  X  177  =  177,000  lb.  X  inch 
/  =  97,000  lb.  mass  X  inch- 

v/e  shall  have 

do:       177,000       .  oo  1  /       2 

Tt  =  ^wm  ^  '•'' '/''" 

This  angular  acceleration  originates  a  linear  acceleration 
in  each  mass  proportional  to  its  distance  from  the  center 
of  gravity  and  in  a  direction  tending  to  oppose  the  rotation 
originated  by  the  couple  C.  Thus,  each  mass  will  be  sub- 
jected to  a  force,  as  illustrated  for  our  example,  in  Fig. 
198a.  It  is  then  easy  to  obtain  the  diagrams  of  the  shear- 
ing stresses  (Fig.  1986),  and  of  the  bending  moments  (Fig. 
198c),  originated  by  the  forces  of  inertia  which  appear  in 
the  various  masses  of  the  fuselage,  when  a  force  of  1000 
lb.  is  suddenly  appUed  upon  the  elevator. 

Let  us  note  that  the  stresses  thus  calculated  are  greater 
than  those  had  in  practice;  in  fact  for  the  calculation  of  the 
angular  acceleration,  the  total  moment  of  inertia  of  the 
airplane  and  not  only  that  of  the  fuselage  should  have 
been  introduced :  therefore  the  angular  acceleration  found 
is  greater  than  the  effective  one.  However  this  approxi- 
mation is  admissible,  since  its  results  give  a  greater  degree 
of  safety. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER  327 


/=  H.H'.Y 
=   100x50x19.4 
=  97.000  lb.  mass.  K  in^ 


Fig.  197. 


328 


AllWLANE  DESIGN  AND  CONSTRUCTION 


0  30000         eOOOO  m/lbs 

Scale  erf  Mo  me  n+^.  MOMENT     DIA6RW4 

r«3.   198. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


329 


(c)  For  maneuvering  the  rudder  the  same  applies  as 
for  the  elevator.  The  same  diagrams  of  Fig.  198  may  also 
be  used  for  this  case. 


SHEAR  DIAGRAM  FORTEN  TIMES  THE  FUSELAGE  WEIGHTS 
fTTTTTTMMIlL  6  ^  8         9         10       II       12      .3 


2         3       4^4'='      5 


Ullllllllllllllllll 


(b) 


SHEAR  DIAGRAM  FOR  762  LBS  ON  ELEVATOR 


rTTTTnTnTTTTTTTIIIII'llhTTi ^ 

2       3      4*^  4"      5 


&        9        10        II        12     13 

"' '"" '""Tin] 


(c) 


SHEAR  DIAGRAM  FOR  300 LBS. ON  RUDDER 


'SHEAR  DIAGRAM   FOR  COMBINATION  OF 
RUDDER  AND  ELEVATOR  LOADS  AND  TEN  TIMES  THE 
FUSELAGE  WEIGHTS. 


{d)  In  order  to  calculate  the  maximum  breaking  stresses 
in  flight,  let  us  suppose  that  the  breaking  load  is  applied  at 
the   same   time   upon   the   wings,    the   elevator,    and  the 


330 


AiRPLAXE  desk;::  and  coxstruction 


rudder.      This     is     equivalonl     to     make     the     following 
hypothesis : 

1.  to  multiply  the  loads  of  the  fuselage  by  10, 

2.  to  apply  762  lb.  upon  the  elevator, 

3.  to  apply  309  lb.  upon  the  rudder. 


0  30  60  In 

Scale  of    Lengths 


0  30000       (60000   /lbs. 

Scale  of   Moments 


2        3       4«  4"       5  6  7  ^  9        10       II        12 

MOMENT    DIAGRAM  FOR  TEN  TIMES  THE  FUSELA6E 
WEIGHTS  ONLY. 


2        3        4a4'>       5  6  7  8         9  10        11         12      13 

MOMENT   DIAGRAM    FOR  762  POUNDS  ELEVATOR 
LOAD    ONLY. 


(^) 


■^..rnTTlT!^ 


2       3       4a    4b        5  e  7  8  9         10        II  12 

MOMENT    DIAGRAM   FOR  306  POUNDS  RUDDER  LOAD 
ONLY. 

FiQ.  200. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


331 


MOMENT  DIAGRAM    FOR   ELEVATOR    LOADS  AND  TEM 
TIMES    THE    FUSELAOE  WEIGHTS 


0  40000  80OOO   /bs. 

Scale  of   Moments 


2       3 

MOMENT    DIAGRAM     FOR     COMBINATION    OF    ELEVATOR 
AND  RUDDER  LOADS  AND  TEN  TIMES  THE  FUSALASE  WEIGHTS 


Fig.  201. 


332  AIRPLANE  DESIGN  AND  CONSTRUCTION 

It  is  then  easy  to  draw  the  diagrams  of  the  shearing 
stresses  in  this  case  (Fig.  199,  a,  b,  c),  and  consequently, 
through  their  sum,  the  diagram  of  the  total  shearing 
stresses  in  flight  (Fig.  199rf). 

In  order  to  calculate  the  maximum  bending  moments, 
it  is  necessary  to  consider  separately  those  produced  by 
vertical  forces  (loads  on  the  fuselage  and  on  the  elevator), 
and  those  produced  by  horizontal  forces  (loads  on  the 
rudder).  In  Fig.  200  a,  b,  c,  the  bending  moments  are 
shown  due  respectively  to  10  times  the  loads  on  the  fuse- 
lage, to  the  load  of  762  lb.  on  the  elevator,  and  to  the  load 
of  306  lb.  on  the  rudder. 

Fig.  201a  shows  a  diagram  obtained  by  the  algebraic  sum 
of  the  first  two  diagrams,  Fig.  2016  shows  the  total  dia- 
gram whose  ordinates  m"  are  equal  to  the  hypotenuses  of 
the  right  triangles  having  the  sides  corresponding  to  the 
ordinates  m  and  m'  of  diagrams  200c  and  20 la. 

Having  obtained  in  this  manner,  the  diagrams  of  the 
maximum  shearing  stresses  and  maximum  bending  mo- 
ments corresponding  to  the  various  sections,  it  is  possible 
to  proceed  in  the  checking  of  the  resistance  of  those  sections. 

In  Fig,  202  the  checking  for  section  4-5  has  been  effectu- 
ated. For  simplicity  it  is  customary  to  assume  that  the 
longerons  resist  to  the  bending  and  the  veneer  sides  to 
the  shearing  stresses.  The  stress  due  to  shearing  is  given 
immediately,  dividing  the  maximum  shearing  stress  by  the 
sections  of  the  veneer.  As  for  the  stresses  in  the  longerons, 
it  is  necessary  to  determine  their  ellipse  of  inertia. 

Let  1,  2,  3  and  4  be  the  four  longerons  constituting  section 
4-5.  The  maximum  moment  is  equal  to  216,600  in.  lb., 
and  its  plane  of  stress  makes  an  angle  a  with  the  vertical 
plain  such  that 

,         _  Horizontal  moment  _    16,400   _  ^  ^^^ 
^^""^  ~  "Vertrcalmoment     ~  215:300  ~  """^^ 

Then  a  certain  section  is  fixed  for  the  longerons  and  with 
the  usual  methods  of  static  graphics  the  moments  of  inertia 
of  the  four  assembled  longerons  with  respect  to  horizontal 
axis  and  to  a  vertical  axis  passing  through  the  center  of 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 
30.70  Jn- 


333 


(a)   TRANSVERSE    SECTION  AT  4-5 


J 

v.y=  725 

J^^     . 

"" 

A 

■ 

X 

^^ 

i 

/ 

/ 

k 

i 

/ 

►.^ 

i 

1 

o' 

U-i- 


0  6  12  In 

Scale    of   Lengths. 


I    I    I 


0  400  "600  In. 

Scale   of 
Ellipse  of  Inertia 


X\    //   /  /     \  \   ^.    /// 


Tan  ex. 


Mh        16400 
Mv    ""   215300 

Ir  =  825  in"^ 


{b)  ELLIPSE  OF  INERTIA    AT  SECTION    4^5 

Maximum  Momenf  ai- SccHon  216600  in  lbs. 
Maximum  Exireme  Fiber  Stress  =    ^.^^     -4470 lbs/in^ 
Modulus  of  Rupture  for  Spruce  =3700  lbs/in^ 
Facf or  of  Safety    -^-x  10=217 
Fio.  202. 


334  AIRPLANE  DESIGN  AND  CONSTRUCTION 

gravity  of  the  system  are  determined  (Fig.  202a).  Then 
the  eUipse  of  inertia  may  be  drawn  (Fig.  2026).  The  vector 
radius  O'A'  of  such  an  eUipse  which  makes  the  angle  a  with 
the  vertical  gives  the  moments  of  inertia  to  be  used  in  the 
calculations.  In  order  to  have  the  section  modulus,  it  is 
necessary  to  draw  B'O'  the  conjugate  diameter  to  O'A'. 
From  the  center  of  gravity  0  of  the  four  longerons  draw  OB 
parallel  to  diameter  O'B';  from  the  four  points  Mi,  Mn,  Ms, 
and  Mi  draw  the  parallels  to  OA,  to  meet  the  straight  line 
OB  in  A^i,  A^2,  N3  and  N^.  By  dividing  the  moments  of 
inertia  measured  by  O'A'  by  the  largest  of  the  4  segments 
MiNi,  M2N2,  M3N3,  MiNi  the  section  modulus  Zr  is 
obtained.  We  can  then  compute  the  unit  stresses  and 
therefore  the  coefficient  of  safety. 

(e)  In  landing,  the  fuselage  is  supported  by  the  landing 
gear  and  by  the  tail  skid.  The  system  of  acting  forces, 
with  coefficient  1,  is  then  that  shown  in  Fig.  203. 

Fig.  204  shows  the  diagrams  of  the  shearing  stresses  and 
bending  moments  corresponding  to  that  case.  Since,  as 
it  will  be  seen,  the  coefficient  of  resistance  of  the  landing 
gear  is  usually  taken  between  5  and  6,  it  will  suffice  to 
multiply  the  preceding  stresses  by  6  and  verify  that  the 
sections  of  the  fuselage  are  sufficient.  In  our  case  these 
stresses  result  lower  than  the  maximum  considered  in  flight. 

B.  Analysis  of  Landing  Gear. — Let  us  consider  the 
following  particular  cases: 

1.  Normal  landing  with  airplane  in  line  of  flight. 

2.  Landing  with  tail  skid  on  the  ground. 

3.  Landing  on  only  one  wheel;  that  is,  with  the  machine 
laterally  inclined  by  the  maximum  angle  which  can  be 
allowed  by  the  wings. 

4.  Landing  with  lateral  wind. 

Figs.  205,  206,  207  and  208  illustrate  respectively  the 
construction  for  those  four  cases,  giving  for  each  the  ten- 
sion on  compression  stresses,  the  diagrams  of  the  bending 
moments,  and  the  member  subjected  to  bending  (axle  and 
spindle).  In  the  fourth  case  it  has  been  assumed  that  the 
maximum  horizontal  stress  is  not  greater   than   400   lb. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER  335 


15,—' 


FiQ.  203. 


336  AIRPLANE  DESIGN  AND  CONSTEVCTION 


3r      A  r 

1         ^ 

.5    s        <b    t 

7R      8::      9c     lot 
o           h^          V£)         <• 

lie     125 

SHEAR      DIAGRAM 


o  7500        15000   in. lbs 

Scale  of    Momen+s 


MOMENT       DIAGRAM, 
FiQ.  204. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


337 


C^SE.  1 


SIDE  ELEVATION 

DIAGRAM 
OF 
LANDING    GEAR 


HALF  FRONT  ELEVATION 

llMllM,,! 


0  20  40in. 

Scale  of  Lenqths.. 


FORCE   POLYGONS 


9      I 


0  300  600  lb&. 

Scale  of    Forces 


in, 


I3.7&  i 


SPACE    DIA&RAM 
FORCES  ACT1N5  ON 
SPINDLES 


0  10  20in. 

Scale  of  Lencj+hs. 


AXLE    MOMENT    DIAGRAM 


Fig.  205. 


4000        8000  /lb 


Scale    of    Mome.nf& 


338 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


CASE  2. 


SIDE    ELEVATION 
DIAGRAM     OF    LANDING  GEAR 

500  LBS. 


HALF    I 
FRONT  ELEVATION 

ml 


(b) 


O  20  40in. 

Scale   of    Lengths 


FORCE  POLYGONS 


hi. 


Mill 


0  300  600 

Scale    of    Forces 


I 


SPACE     DIAGRAM  FORCES  ACTING 
ON  SPINDLES. 


J L 


AXLE     MOMENT    DIAGRAM 


O  10  20  in. 

Scale   of    Lengths 


Fig.  206. 


I ml I lirv 

0  4000       eooo/ib; 

Scale  of  Moments 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 
CASE    3 


339 


SIDE   ELEVATION 
DIAGRAM    OF  LANDIN66EAR 


HALF  FRONT  ELEVATION 


lllllllllll 


0  20  40In. 

Scale  of  Len^+hs. 


li'Mlmil         f        t 
0  600  1200  lbs, 

Scale  of  Fores© 


0  6000         KOOOIn.lbs. 

Scale  of  Moments 


?IG.  207. 


340 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


because  with  a  great  transversal  load  the  wheel  would 
break.  In  Fig.  209  the  sections  of  the  various  members 
have  been  given,   the  results  of  the  analysis  having  been 

CASE    4-. 


FRONT    eLevATION 


SIDE       ELEVATION 


Scale     o-F    Leng+hs 
400  lbs. 


D1A6R^M  OF  ENDING  6EAR 


FORCE 
<S,  POLYGONS 


0  200  400  Iba 

Scale    of     Forces. 


Fig.  208. 

grouped  in  table  44.     The  table  gives  the  following  elements 
for  each  member: 

P  =  compression  or  tension  stress 
Mf  =  Bending  moment 
/  =  Moment  of  inertia 
Z  =  Section  Modulus 
A  =  Area  of  the  section 
Fc  =  unit  load  due  to  compression  or  tension 
F„  =  Unit  load  due  to  bending 
Ft  =  Total  unit  load 
Modulus  of  rupture 
Coefficient  of  safety 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


341 


1 

°^ 

l>Tt<ir3iOt^Tj<00000»OOOOfOOOOOO 

II 

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S8§:2§SSS§8§S     8§§:2 

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f^^^ 

2' 8"^'     2^8""^"     2^8'"'""        S'S^"^' 

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j3                                               -^ 

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85    :    :g5    :    :8  8    :    :8S§    :    :i   1 

^£^ 

19,2 
11,0 

19,2 
11,0 

27,7 
14,8 

,h  2,0 
5 

h  2,01 

bJ3                                hO 

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oT  cT   .■    i  oT  o    !    ;  r>r  rtT    :    :  "^            :    :  "> 

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342 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


As  for  the  criterions  to  be  followed  in  the  selection  and 
computation  of  the  shock  absorbers,  reference  is  to  be 
made  to  what  has  been  said  in  Chapter  XVI. 


SECTION!  A- A, 


SECTION  S-B. 

Fig.  209. 


SECTION  C-C  AND  D-D. 


C.  Analysis  of  the  Propeller. — In  the  following  chapter 
it  will  be  seen  that  for  the  airplane  of  our  example  the 
adoption  of  a  propeller  having  a  diameter  of  7.65  ft.  and  a 
pitch  of  9  ft.  is  convenient.  We  shall  then  see  the  aero- 
dynamic criterions  which  have  suggested  that  choice.  In 
this  chapter  we  shall  limit  ourselves  to  static  analysis  of  the 
propeller.  This  static  analysis  is  usually  undertaken  as  a 
checking;  that  is,  by  first  drawing  the  propeller  based  upon 
data  furnished  by  experience  and  afterward  verifying  the 
sections  by  a  method  which  will  be  explained  now. 

Supposing  a  propeller  is  chosen  having  the  profile  shown 
in  Figs.  210,  211,  212  and  213. 

Fig.  210  gives  the  assembly  of  only  one  half  the  propeller 
blade  the  other  half  being  perfectly  symmetrical.  Further- 
more it  gives  six  sections  of  the  propeller  which  are  repro- 
duced on  a  larger  scale  in  Figs.  211,  212  and  213.     It 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


343 


CM     «^     ^     W^     VO 


344 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Q  J  2  3 


Scale  of  Inches 
Fig.  211. 


/V 


V 

N^ 

\ 

h'0.72  ,n 
A=  7.37aq.in 

\ 

N 

S^ 

<^ 

^ 

Ip-  19.7, ni 
Zp-S.ldm^ 

\ 

1 

\> 

\ 

V 

:> 

y 

Scale  of  Inche 
Fig.  212. 


<: 

! 

h-  072  in 
A-  4.03sq.m. 

\ 

^ 

'^^ 

-k 

H 

^ 

Ip- 9.79  m* 
Zp-2.57m.^ 

4"; 

^ 

^^ 

:^' 

i 

^'-- 

> 

0  18  3 


I 

h  -  055  in. 
A-  1.44  sqm 

/^ 

^^ 

Ip- 2.18  m'' 
7p-0.80m^ 

^ 

^ 

^ 

^ 

^ 

> 

r:: 

^ 

0 

' 

s        ^ 

5 

3              7 

Scale  of  Inches 
Fig.  213. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER  345 

should  be  noted  that  in  that  type  of  propeller  the  pitch  is 
not  constant  for  the  various  sections,  but  increases  from 
the  center  toward  the  periphery  until  the  maximum  value 
of  9  feet  is  reached  which  is  the  one  assumed  to  characterize 
the    propeller. 

The  forces  which  stress  the  propeller  in  its  rotation  can 
be  grouped  into  two  categories: 

1.  Centrifugal  forces  which  stress  the  various  elements 
constituting  the  propeller  mass. 

2.  Air  reactions  which  stress  the  various  elements  consti- 
tuting the  blade  surface. 

If  any  section  A  of  the  propeller  is  considered,  the  forces 
which  stress  that  section  are  then  the  resultants  of  the 
centrifugal  forces  and  the  resultants  of  the  air  reactions 
pertaining  to  that  portion  of  the  propeller  included  between 
section  A  and  the  periphery.  In  general,  these  resultants 
do  not  pass  through  the  center  of  gravity  of  section  A, 
so  their  action  on  that  section  produces  in  the  most  general 
case: 

1.  Tension  stresses. 

2.  Bending  stresses. 

3.  Torsion  stresses. 

It  is  immediately  seen  that  by  giving  a  special  curvature 
to  the  neutral  axis  or  elastic  axis  of  the  propeller  blade  it  is 
possible  to  equilibrate  the  bending  moment  in  each  section 
produced  by  the  centrifugal  force,  with  that  produced  by 
the  air  reaction. 

The  stresses  will  then  be  those  of  tension  and  torsion, 
resulting  thereby  in  a  greater  lightness  for  the  propeller. 

We  shall  then  proceed  to  find  the  total  unit  stresses  and 
the  curvature  to  be  given  to  the  neutral  axis  of  the  propeller 
blade.  In  order  to  proceed  in  the  computations,  it  is 
necessary  to  fix  the  following  elements : 

N  =  number  of  revolutions  of  the  propeller, 
CO  =  corresponding   angular   velocity, 
Pp  =  power  absorbed  by  the  propeller  when  turning  at 
A^  revolutions, 


346  AIRPLANE  DESIGN  AND  CONSTRUCTION 

A  =  density  of  the  material  out  of  which  the  propeller  is 
to  be  made. 

In  our  case,  N  =  1800,  and  therefore 

CO  =  2j^  =  188  1/sec. 
oO 

Furthermore  Pp  =  300  H.P. 

As  for  the  material,  the  propellers  can  be  made  of  walnut, 

mahogany,  cherry,  etc.     Suppose  that  we  choose  walnut, 

for     which   A  =  0.0252    lb.    per    cu.    in.     Let     us     now 

find   the   expression   for   the   centrifugal   force   d^   which 

stresses  an  element  of  mass  dM,  and  for  the  reaction  of 

the  air  dR  which  stresses  an  element  IdSoi  the  blade  surface. 

The  elementary  centrifugal  force  d^  has,  as  is  known,  the 

expression 

d^  =  dM  X  CO-  X  r 

since  w^e  can  place 

dM  =  ^  X  A  X  dr 

g 

where 

g  is  the  acceleration  due  to  gravity  =  386  in. /sec. 2, 
A  is  any  section  whatever  of  the  propeller,  and 
dr  is  an  infinitesimal  increment  of  the  radius. 
We  shall  then  have 

d^  =  "^  X  i^-  X  A  X  r  X  dr 
9 
=  2.^  X  A  X  r  X  dr 
from    which 

^  =  2.3  X  A  X  r  (1) 

dr 

Then  by  determining  the  areas  of  the  various  sections  A, 
we  shall  be  able  to  draw  the  diagram  A  =  f  (r)  of  Fig.  214, 
which  by  means  of  formula  (1)  permits  drawing  the  other 
one 

d^       .,  . 

whose  integration  gives  the  total  centrifugal  forces  $ 
which  stress  the  various  sections  (Fig.  215). 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


34< 


The  elementary  air  reaction  dR  has  the  following  expres- 
sion 

dR  ==  KXdS  X  t/2 

where  K  is  a  coefficient  which  depends  upon  the  profile  of 
the  blade  element  and  upon  the  angle  of  incidence,  dS  is  a 


16        20        24        2&         32         36 
Radii  -in  Inches 


surface  element  of  the  blade,  and  U  is  the  relative  velocity 
of  such  a  blade  element  with  respect  to  the  air. 

Calling  I  the  variable  width  of  the  propeller  blade,  we  may 
make 

dS  ^  I  X  dr 


Fig.  215. 

on  the  other  hand,  velocity  U  is  the  resultant  of  the  velocity 
of  rotation  r  and  of  velocity  of  translation  V,  of  the  air- 
plane. The  direction  of  these  velocities  being  at  right 
angles  to  each  other  we  shall  have 

[/2  =  0,2  X  r2  +  F2 


348  AIRPLAXE  DESIGN  AND  CONSTRUCTION 

therefore 


(IR  =  K  X  (co^  Xr-  +  Y'-)  XlXdr 


from  which 


dR 
dr 


=  KX  {o:-  X  r-  +  V)  X  I 


It  is  iminediately  seen  that  it  would  be  very  difficult  to 
take  into  consideration  the  variation  of  coefficient  K 
from  one  section  to  the  other,  and  therefore  with  sufficient 


Fia.  216. 

practical  approximation  K  may  be  kept  constant  for  the 
various  sections  and  equal  to  an  average  value  which  will 
be  determined. 

We  note  that  dR  being  inchned  backward  by  about  4° 
with  respect  to  the  normal  to  the  blade  cord,  changes 
direction  from  section  to  section;  it  will  consequently  be 
convenient  to  consider  the  two  components  of  dR,  com- 
ponent dRt  perpendicular  to  the  plane  of  propeller  rotation 
and  component  dRr  contained  in  that  plane  of  rotation 
(Fig.  216). 

The  expression  -j-  can  also  be  put  in  the  following  form : 


dr 


X  (r^  +  -')  X  ^ 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER  349 


350  AIRPLANE  DESIGN  AND  CONSTRUCTION 

In  our  case  to  =  188  and  V  =  156  m.p.h.  =  2800  in. 
per  sec.  (see  page  374  for  \'alue  of  V). 

On  an   axis  ^A^  lay   off  the  various  radii   (Fig.  217), 

make  AB  ^     -  =    loo    =  14.9  perpendicular  to  AX,  and 

from  B  draw  segment  BC.     We  shall  evidently  have 

BC'  =  AB'  +  AC' 
that  is, 

BC'  =  ^  +  r' 

Analogously   by   drawing   BC,  BC",  etc.  the   squares   of 

V- 
these  segments  will  give  the  terms  — r  +  r^.     In  this  manner 

~jj  may  be  calculated,  except  for  the  constant  K. 

Make   ,.  equal  to  CD,  so  that  CD  makes  an  angle  of  4° 

with  the  prolongation  of  BC.     Projecting  D  in  E  and  F, 

we  shall  have 

dRr       ,  dRt 

DE  =  -,     and  DF  =  -y- 

dr  dr 

We  may  then  draw  the  two  diagrams 

-^-=/(r)   and-^^-=/(r) 

whose  integration  gives  the  value  of  components  Rr  and  Rt 
corresponding  to  the  various  sections;  that  is,  gives  the 
shearing  stresses.  For  clarity,  these  diagrams  have  been 
plotted  in  two  separate  figures  for  components  Rr  and  Ri, 
the  former  having  been  plotted  in  Fig.  217  and  the  latter 
in  Fig.  218. 

The  shearing  stresses  Rr  and  Rt  being  known,  by  means 
of  a  new  integration,  the  diagrams  of  the  bending  moments 
Mr  and  M«  can  easily  be  obtained.  It  should  be  noted 
that  the  maximum  value  of  Mr  equals  one-half  of  the  motive 
couple.  The  power  being  300  H.P.  and  the  angular  velocity 
w  =  188,  the  motive  couple  will  equal 

QfU)  V    r^rn 

188        "  ^^^^  "'•  ^  ^^"  ^  ^^'^^^  ^^'-  ^  "'''^ 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


351 


352 


AIRPL.WE  DESiaX  AND  CONSTRUCTION 


therefore 

Mr  =  I  X  1 0,500  11).  X  inch  =  5280  lb.  X  mch. 
The  scale  of  moments  is  fixed  in  this  manner  and  conse- 
quently that  of  the  shearing  stresses;  and  thus  the  value  of 
the  coefficient  A'  is  also  determined.  Then,  for  each  section, 
the  resultant  stress  due  to  the  centrifugal  force,  the  shearing 
stresses  Rr  and  Rt,  and  the  moments  Mr  and  M<  due  to  the 
air  reaction,  are  known. 

If  the  moment  produced  in  any  section  whatever  by 
the  centrifugal  force  is  somehow  made  to  be  in  equilib- 
rium with  the  moments  Mr  and  Mt,  the  deflection  stresses 
will  be  avoided. 


Trac€  of  ftJt  Ptant  of  f*ofafion 


V  -    y/zlocttij  of  Aeroolana 


Let  us  first  of  all  consider  the  moments  Mt  which  are  the 

greatest  and  consequently  the  most  important,  especially 

because  they  stress  the  blade  in  a  direction  in  which  the 

moment  of  inertia  is  smaller  than  that  corresponding  to 

the  direction  in  which  the  blade  is  stressed  by  the  bending 

moments  Mr. 

dy 
Let  us  call  -p  the  inclination  of  any  point  whatever  of 

the  neutral  axis  curve  of  the  propeller.  We  shall  then 
consider  any  section  A  whatever  of  the  propeller  blade, 
and  the  elementary  forces  d^  and  dR  applied  to  it.  The 
elementary  force  d^  follows  a  radial  direction,  while  the 
elementary  force  dRt  follows  a  direction  perpendicular  to 
the  plane  of  rotation  of  the  propeller  (Fig.  219);  while 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


353 


d$  is  applied  to  the  center  of  gravity  of  the  element  A  X 
dr,  the  air  reaction  dRt  is  not  applied  to  the  center  of  gravity, 
but  falls  at  about  33  per  cent,  of  the  chord.  However,  from 
known  principles  of  mechanics,  this  force  can  be  replaced 
by  an  elementary  force  dRt  applied  to  the  center  of  gravity, 
and  by  an  elementary  torsion  couple  dTt.  The  effect  of  this 
couple  will  again  be  referred  to,  and  for  the  moment  we  shall 
suppose  dRt  applied  to  the  center  of  gravity.  Let  us 
assume  then  the  condition 

d$  _  dy 

dRt  ~  dr 


Fig.  220. 

that  is,  that  the  resultant  of  c?$  and  dRt  be  tangent  to  the 
neutral  curve  of  the  propeller  blade.  Under  these  condi- 
tions, supposing  that  this  be  true  for  every  element 
A  X  dr  of  the  propeller,  all  the  various  sections  will  be 
stressed  only  to  tension. 
Since  we  may  write 

d^  _  d^/dr 
dRt  ~  dRt/dr 
it  is  easy  to  draw  the  diagram 

f  =  /« 

and,  by  graphically  integrating  this  diagram,  obtain 

y  =f{r) 

which  gives  the  shape  that  the  center  of  gravity  axis  of  the 
propeller  blade  must  have  in  elevation  (Fig.  220). 


354 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


With  an  analogous  process,  the  shape  in  plan  is  found 

by  considering  the  forces  d^  and  dRr]  in  Fig.  221  the  rela- 

dv 
tive  diagrams  have  been  drawn  for  ,     =  /(r)  and  y  =  /(r). 

Thus  the  propeller  may  be  designed.     In  Fig.  210  the  neu- 
tral axis  has  been  drawn  following  this  criterion. 


1 
j 

\ 

|jr^ 

^ 

.^: 

-4- 

--U 

T 

i 

i 

M  24  2G 

Radii  in  Inches 


-fk 


Let  us  now  determine  the  unit  stresses  corresponding  to 
the  case  of  normal  flight. 

These  stresses  are  of  two  types: 

1.  tension  stresses, 

2.  torsion  stresses. 


1 600 

i 

-^  400 


200 


0 

1 

i 

n 

: 

3 

! 

4 

; 

6 

j 

— 

/ 

"^ 

^ 

^¥ 

R?'R? 

1 
i 

! 

^ 

^v 

/ 

''    1 
i 

^ 

1 

I 

1 

/ 

1 
i 

1  ^ 

\^ 

1 

i 

i 
1 

K, 

i 
i 

s 

Ni 

1 
i 

i 

s, 

20  24         28 

Radii  in  Inches 


Tension  stresses  are  easily  calculated,  in  fact,  for  every 
section  A  they  are  equal  to 

f,  = _ _ 

In  Fig.  222  the  diagram  of  /i  obtained  by  the  preceding 
equation  has  been  drawn. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER 


355 


As  to  the  torsion  stresses,  they  depend  only  upon  the 
air  reaction.  Let  us  consider  a  section  A  and  the  air  reac- 
tion dR  which  acts  upon  the  blade  element  I  ■  dr  correspond- 
ing to  this  section.     Evidently 

dR  =  {dR:-  +  dRr')^- 
The  point  of  application  of  dR  falls,  as  we  have  seen,  at  0.33 
of  the  width  of  the  blade  l;  therefore  dR  will  in  general 
produce  a  torsion  about  the  center  of  gravity;  let  us  call 


Fig.  223. 

h  the  lever  arm  of  the  axis  of  dR  with  respect  to  the  center 
of  gravity;  the  elementary  torsional  moment  will  be 

dT  =  hX  dR  =  hX  idR^  +  dRr^y' 
and  consequently 

f-x[(fr-(fi 

The  values  of  h  are  marked  on  the  sections  (Figs.  211,  212 

and  213) ;  the  values    ,-  and  -~  are  given  by  the  diagrams 

of  Figs.  217,  218;  thus  in  Fig.  223  the  diagram  may  be 
drawn  of 

dT       «.  V 

and  by  integrating,  that  of 

T  =  fir) 


356  AIRPLANE  DESIGN  AND  CONSTRUCTION 

0  12  3  4  5  6 


48 
40 
32 

~'    16 


1400 


400 

?00- 
0: 


16       20       24      28       32       36      40     44 
Fig.  224. 
2  3  4  5  6  . 


1 

j 

1 

1 

! 

! 

1 

i 

^ 

< 

1 

k 

i 
i 

/ 

1 

i 

\| 

^ 
j 

/ 

1 

1 

1 

j 

) 

i 
i 

! 

1 

i 
1 

i 

40 
32 

16  5 


16       20       24 
Fig.  225. 


32        36       40       44 


16       20       24       28       32       36      40       44 


Fig.  226. 


FUSELAGE,  LANDING  GEAR  AND  PROPELLER  357 

It  is  now  necessary  to  determine  the  polar  moments  Ip 
of  the  various  sections ;  to  this  effect  it  suffices  to  determine 
the  ellipse  of  inertia  of  the  various  sections  by  the  usual 
methods  of  graphic  analysis;  then  calling  I^  and  ly  the 
moments  of  inertia  with  respect  to  the  principal  axis  of 
inertia,  we  will  have 

/,  =  {IJ  +  Iy^y 
For  each  section  (Figs.  211,  212  and  213),  we  have  shown 
the  values  of  the  area,  of  the  polar  moment  Ip  and  of  Zp  = 

—■     In  Fig.  224  the  diagram  Ip  for  the  various  sections  and 
the  diagram  --  =  Zp  have  been  drawn. 

Dividing,  for  each  section,  the  corresponding  values  of 
the  total  moment  of  torsion  T  by  the  values  of  the  section 
modulus  for  torsion  Z,  we  shall  have  the  values  /2  of  the 
unit  stresses  to  torsion  (Fig.  225).  It  is  immediately  evi- 
dent that  this  method  is  exact  only  when  the  neutral 
axis  of  the  propeller  is  rectilinear  and  in  the  direction 
of  the  radius,  which,  however,  does  not  correspond  to 
practice.  In  effect  though,  as  the  torsion  stresses  represent 
a  small  fraction  of  the  total  stresses,  the  approximation 
which  can  be  reached  is  practically  sufficient. 

When  the  unit  stresses  /i  and  /a  to  tension  and  torsion 
are  known,  the  total  stress  ft  is  determined  by  the  formula 

ft  =  0.35  X  /i  +  0.65  X  ifi'  +  4  X  a^-  X  /2^)^' 
where 

^      modulus  of  rupture  in  tension       _  ,^  7 
1 .3  modulus  of  rupture  in  shearing 

Then  the  diagram  which  gives  ft  for  the  various  sections 
may  be  drawn  (Fig.  226).  It  is  seen  that  the  value  of  the 
maximum  stress  is  equal  to  1280  pounds  per  square  inch; 
that  is,  to  about  I9  the  value  of  the  modulus  of  rupture. 

As  a  safety  factor  between  4  and  5  is  practically  suffi- 
cient for  propellers,  it  may  be  concluded  that  the  aforesaid 
sections  are  sufficient. 


CHAPTER  XX 

DETERMINATION  OF  THE  FLYING 
CHARACTERISTICS 

Once  the  airplane  is  calculated  and  designed,  it  becomes 
possible  to  determine  its  flying  characteristics.  The  best 
method  for  this  determination  would  undoubtedly  be  that 
of  building  a  scale  model  of  the  designed  airplane  and  of 
testing  it  in  an  aerodynamic  laboratory.  This,  however, 
is  often  impossible,  and  it  is  therefore  necessary  to  resort 
to  numerical  computation. 

Let  us  remember  that  the  aerodynamical  equations  bind- 
ing the  variable  parameters  of  an  airplane  are 

W  =  10-''  \AV'   and 
550Pi  =  L47  X  10-^5^  +  <r)V' 
where 

W  =  weight  in  pounds, 
A  =  surface  in  square  feet, 
V  =  speed  in  miles  per  hour, 

Pi  =  theoretical  power  in  horsepower  necessary  for  flight, 
0-  =  coefficient  of  total  head  resistance,  and 
X  and  8  =  coefficient  of  sustentation  and  of  resistance  of 
the  wing  surface. 
Let  us  assume,  as  m  Chapter  VIII,  that 
A  =  10-"  \A 

A   =    10-^5.-1    +  a) 
The  preceding  equations  can  then  be  written 


W 
V 
550Pi 


y"2  =^ 


=  1.47  A 


Since  A  and  a  are  constant  and  X  and  8  are  functions  of 
the  angle  of  incidence  i,  A  and  A  will  also  be  functions  of  i. 

358 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS     359 


o 

>  cL- 

\ 

s. 

s 

s 

"^V~~ 

--  o^    \ 

mmb 

= 

^ 

: 

^^ 

= 

= 

■:zzi 



fefr 

1 

izz: 

: 

z^ 

§ 

^ 

P 

1 

= 

'ZZZ. 

:z^ 

EEESE--L^ 

/ 

\ 

^ 

: 

Z  — 

::. 

.^^ 

X 

E 

= 

= 

= 

•is-*-^ 

=  =      V- 



V 





-■ 

^ 

\ 







^± 

— 

A 

— 

— 

r 

- 

^ 



— 

\ 

_ 

-N 

'  \^ 

<-.\o 

o:^ 

;>^ 

S^Q^ 

s. 

^   \ 

^ 

_^Sv:. 

\ 

-^ 

s^\W 

^ 

s- 

iX 

\, 

s 

v"^ 

s 

v> 

\ 

rv-'^^ 

N^ 

s 

s' 

n^ 

~ 

°« 

V 

°c.^ 

-<> 

'; 

-^ 

r- 

\ 

'  '\::. 

(^ 

\ 

K 

•{ 

iS 

s\ 

s 

\ 

. 

\ 

\^ 

^\^ 

o 

\ 

f;f-X=^r. 

\, 

s,^/^ 

^^^^'v. 

\ 

V 

s 

N 

A 

A% 

\ 

^ 

\ 

N.^ 

A 

!o 

CV 

i 

S 

\ 

s 

■■■% 

"■y  \ 

^ 

s 

\ 

^    ' 

Q 

s\ 

S  - 

^ 

ll^' 

\ 

A 

% 

A 

A... 

360 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Then,  X,  5  and  o-  being  known,  it  is  possible  to  obtain  a 
pair  of  values  of  A  and  A  corresponding  to  each  value  of 
i,  and  the  logarithmic  diagram  of  A  as  function  of  A  can 
then  be  drawn. 

Let  us  suppose  that  X  and  8  are  given  by  the  diagram  of 
Fig.  155  (Chapter  XVII).  The  value  of  a  is  calculated  by 
remembering  that 

cr  =  2X  X  .4 

that  is,  it  is  equal  to  the  sum  of  the  head  resistances  of  the 
various  parts  of  which  the  airplane  is  composed.  This, 
however,  does  not  always  hold  true,  because  of  the  fact 
that  the  head  resistance  offered  by  two  or  more  bodies  close 
to  each  other  and  moving  in  the  air  is  not  always  equal  to  the 
sum  of  the  head  resistances  the  bodies  encounter  when  mov- 
ing each  one  separately,  but  it  can  be  either  greater  or 
smaller.  Thus,  an  exact  value  of  the  coefficient  <r  can  be 
obtained  only  by  testing  a  model  of  the  airplane  in  a  wind 
tunnel.  However,  if  such  experimental  determination  can- 
not be  available,  the  value  <r  can  be  determined  approxi- 
mately by  calculation  as  has  been  mentioned  above.  Table 
45  shows  the  values  of  K,  A  and  K  X  A  for  the  various  parts 
constituting  the  airplane  in  our  example.  This  table  gives 
a  =  132.5.  It  is  then  easy  to  compile  Table  46  which  gives 
the  couples  of  values  corresponding  to  A  and  A  and  con- 
sequently enables  us  to  draw  the  logarithmic  diagram  of  A 
as  function  of  A  (Fig.  227). 


Table  45 


Fuselage 

Cables 

Struts 

Landing  gear . . . 

Wheels 

Control  surfaces 


:KA  =  132.5 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS      361 


The  scales  of  W,  Pi  and  V  of 
this  diagram  are  easily  found  with 
processes  analogous  to  those  used  in 
Chapters  VIII  and  IX. 

The  diagram  then  enables  us  to 
immediately  find  the  pair  of  values 
V  and  Pi  corresponding  to  sea 
level;  this  makes  possible  the  im- 
mediate determination  of  the  maxi- 
mum speed  which  can  be  reached. 
Thus  it  is  necessary  to  know  the 
power  of  the  engine  (which  in  our 
case  is  300  H.P.)  and  the  propeller 
efficiency;  supposing,  as  it  should 
always  be,  that  the  number  of  re- 
volutions of  the  propeller  may  be 
selected,  we  can  reach  an  efficiency 
of  p  ==  0.815;  then  the  maximum 
useful  power  is  0.815  X  300  =  244 
H.P.;  making  Pi  =  244  we  have 
A' A"  the  segment  which  represents 
^max.;  laying  this  segment  off  on 
the  scale  of  speeds  we  have  Fmax. 
=  153  m.p.h. 

It  is  also  seen  that  the  minimum 
speed  at  which  the  airplane  can 
sustain  itself  is  given  by  the  seg- 
ment B'B"  which,  read  on  the  scale 
of  speeds,  gives  "Tmin.  =  72  m.p.h.; 
that  is,  it  is  lower  than  the  value 
75  m.p.h.  imposed  as  a  condition. 
Then  our  airplane  can  fly  at  speeds 
between  72  and  153  m.p.h.  If  we 
wish  to  study  its  climbing  speed  it  is 
necessary  to  draw  the  diagram  which 
gives  pPi  as  function  of  the  various 
speeds.  Thus  it  is  necessary  to  know 
the  characteristics  of  the  engine  and 
propeller. 


°o 

19.2 
1.57 
0.509 
550X10-4 

So 

17.8 
1.32 
0.472 
483X10-4 

f. 

16.0 
1.08 
0.423 
428X10-4 

"7 

14.5 
0.88 
0.384 
365X10-4 

Tf     O 

°^^X 

COOOO 

?. 

11.4 
0.60 
0.302 
291X10-4 

n 

10.0 
0.53 
0.265 
274X10-4 

?, 

IN    O 

°  T  =^  X 
00  o  o  r~ 

6.0 

0.43 

0.159 

246X10-4 

h 

4.0 

0.42 

0.106 

244X10-4 

1 

2.3 

0.41 

0.061 

241X10-4 

- 

-<  «.  <  < 

2  2 
II   II 


6^ 
■»  ,< 

CD    O 
IN    " 

II       II 


362 


Alh'l'L.WE  DESIGN  AND  CONSTRUCTION 


Let  us  suppose  that  the  characteristics  of  the  engine  be 
the  same  as  those  given  in  Fig.  228.  We  see  that  the  maxi- 
mum power  of  300  H.P.  is  developed  at  1800  revolutions  per 


■^     240 


:::::::::::::::::::z::::::::::-z 


14  15  16 

Rp.m  (Hundreds) 
Fig.  228. 


minute;  on  the  other  hand,  if  we  wish  to  reach  the  maxi- 
mum efficiency  of  p  =  0.815,  it  is  necessary  to  satisfy  a 
certain  ratio  between  the  translatory  velocity  of  the  air- 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS      363 


plane  and  the  peripheric  velocity  of  the  propeller.  In  Fig, 
71  (Chapter  VI),  which  is  repeated  in  Fig.  229  are  shown 
the  values  of  the  maximum  obtainable  efficiencies  with 


7 

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Fio.   229. 


2.0 


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0.2 


propellers  of  the  best  known  type  to-day,  with  the  indica 
the  value  of  maximum  efficiency,  adopting  as  units,  how 


tion  of  the  values    ~,  a  =     \jy^  and  yz  corresponding  to 


364  AIRPLANE  DESIGN  AND  CONSTRUCTION 

ever,  m.p.h.   for  V,  r.p.m.  for  n,  feet  for  p  and  D,  and 
H.P.  for  P. 

Since  we  want  p  =  0.815,  and  consequently  we  have 
seen  that  Fmax.  =  1^3  m.p.h.,  the  diagrams  of  Fig.  229 
allow  us  to  obtain  the  number  of  revolutions  and  the  diam- 
eter of  the  propeller.     In  fact  for  p  =  0.815  we  find 

^  =  11.4  X  10-3 


1.18 


D 

V 

Knowing  that  V  =  153  and  P  =  300  H.P.  we  have  as 
unknowns  n,  D  and  p,  whose  values  are  defined  by  the 
preceding  equations.     Solving  these  equations  we  obtain: 

n  =  1690  revolutions  per  minute, 
D  =  7.92  feet,  and 
p  =  9.35  feet. 

Since  the  number  of  revolutions  found  is  very  near  to  the 
average  R.p.m.  of  the  engine,  it  will  be  convenient  in  our 
case  to  connect  the  propeller  directly  with  the  crank-shaft. 

Having  obtained  the  propeller,  it  is  necessary  to  know  the 
characteristic  curve  of  the  propeller  family  to  which  it  be- 
longs. It  should  be  remembered  that  all  propellers  having 
the  same  blade  profile  and  the  same  ratio  between  pitch 
and  diameter,  have  the  same  characteristics  (see  Chapter 
IX). 

Let  the  characteristics  of  a  family  to  which  our  propeller 
belongs  be  those  given  in  the  logarithmic  diagram  of  Fig.  230. 
Then  with  the  same  criterions  which  have  been  explained 
in  Chapters,  IX,  XIII,  and  XIV,  it  is  possible  to  draw 
the  diagram  of  pP2  as  a  function  of  V  for  any  altitude ;  for 
instance,  the  altitudes  0,  16,000,  24,000,  and  28,000  ft.  For 
this  purpose  the  diagrams  have  been  drawn  in  Fig.  230, 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS     365 


which  give  the  values  -^ffb  corresponding  to  these  altitudes 
and  in  Fig.  231  the  diagrams  of  P2  of  the  same  heights. 


6x10''^  8)(I0'3        10x10'^    12x10'^  14x10'' 

V 
nD 
60         70       80      90     100  150  200 

t  I  I  I  I  I  I  I  lihiillrtril        I       I      I      I      I     I 


J_U 


V.  m.p.h. 


Fig.  230. 


By  using  these  diagrams  those  of  Fig.  232  have  been 
drawn  from  which  it  is  seen  that  the  maximum  velocity  at 
sea  level  is  only  150  m.p.h.  with  a  corresponding  useful 
power  of  225  H.P.     This  depends  upon  the  fact  that  a  pro- 


366 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


peller  has  been  directly  connected  which  should  have  been 
used  with  a  reduction  gear  having  a  ratio  of  ,  o^„      We  will 


Fio.  231. 


immediately  see  that  if  we  wish  to  adopt  a  direct  connection 
it  is  more  convenient  to  choose  a  propeller  which,  although 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS      367 


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368  AIRPLANE  DESIGN  AND  CONSTRUCTION 

belonging  to  the  same  family,  is  of  smaller  dimensions  so  as 
to  permit  the  engine  to  reach  the  most  advantageous  num- 
ber of  revolutions  and  therefore  to  develop  all  the  power 
of  which  it  is  capable.  It  is  interesting,  however,  to  first 
study  the  behavior  of  the  propeller  having  a  diameter  of 
7.92  ft.  in  order  to  compare  it  to  that  of  a  smaller  diameter. 
The  diagrams  of  Fig.  232  show  that  the  maxinmm  hori- 
zontal velocities  at  the  various  altitudes  with  the  propeller 
of  7.92  ft.  of  diameter  are 

at  0  ft.,  150  m.p.h. 

at  16,000  ft.,  148  m.p.h. 
at  24,000  ft.,  144  m.p.h. 
at  28,000  ft.,  138  m.p.h. 

These  diagrams  allow  us  to  obtain  the  differences  pP2  — 
Pi  and  therefore  to  compute  the  values  of  the  maximum 
chmbing  velocities  v  at  the  various  heights.  These  veloc- 
ities are  plotted  in  Fig.  233;  on  the  ground  the  ascending 
velocity  is  equal  to  29.5  ft.  per  second.  At  28,000  ft.  it 
is  equal  to  1.7  per  second;  that  is,  equal  to  a  Uttle  more 
than  100  ft.  per  minute;  the  height  of  28,000  ft.  must  then 
be  considered  as  the  ceiling  of  our  airplane  if  equipped 
wdth  the  above  propeller. 

From  the  diagram  of  y  =  f{H)  it  is  easy  to  obtain  that  of 

-  =  f{H)  (Fig.  234a),  and  therefore  by  its  integration,  we 

obtain  that  of  t  =  f{H),  which  gives  the  time  of  climbing 
(Fig.  2346).  It  can  be  seen  that  with  this  particular  pro- 
peller, the  airplane  can  reach  a  height  of  28,000  ft.  in  3000 
seconds;  that  is,  in  50  minutes. 

Let  us  now  suppose  that  a  propeller  is  adopted  of  such 
diameter  as  to  permit  the  engine  to  reach  its  maximum 
number  of  revolutions.  By  using  the  diagram  of  Figs.  227 
and  230  we  find  with  easy  trials  and  by  successive  approxi- 
mation that  the  most  suitable  propeller  will  have  a  diam- 

eter  of  7.65  ft.  and  therefore  as  w  =  1.18,  a  pitch  of  about 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS     369 


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370  AIRPLANE  DESIGN  AND  CONSTRUCriON 


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DETERMINATION  OF  THE  FLYING  CHARACTERISTICS      371 


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372  AIRPLANE  DESIGX  AND  CONSTRUCTION 


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DETERMINATION  OF  THE  FLYING  CHARACTERISTICS     373 

.-H  pe  A 


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Fig.  237. 


374  AIRPLANE  DESIGN  AND  CONSTIUCTION 

9  ft.  This  propeller  is  the  one  for  which  the  static  analysis 
was  given  in  the  preceding  chapter.  For  such  a  propeller 
the  logarithmic  diagi-ams  of  pP^,  the  diagram  v  =  f{H)  and 

those  of  -  =  /(//)  and  t  ==  f(H)  have  been  plotted  in  figures 

235,  236  and  237a6  respectively. 

The  diagrams  of  Fig.  235  show  that  the  new  maximum 
velocities  are 

at  0  ft.,  156  m.p.h. 

at  16,000  ft.,  155  m.p.h. 
at  24,000  ft.,  150  m.p.h. 
at  28,000  ft.,  144  m.p.h. 

The  diagram  of  Fig.  236  shows  that  at  an  altitude  of 
28,000  ft.,  V  =  3.7  ft.  per  second  =  222  ft.  per  minute; 
that  is,  the  ceiling  has  become  greater  than  28,000  ft. 

The  diagram  of  Fig.  237  finally  shows  how  the  height  of 
28,000  ft.  is  reached  in  2400  seconds;  that  is,  in  only  40 
minutes. 

The  second  propeller,  therefore,  is  decidedly  better  than 
the  first  one. 

The  question  now  arises:  What  is  the  maximum  load 
that  can  be  hfted  with  our  airplane?  It  is  therefore  neces- 
sary to  suppose  the  efficiency  of  the  propeller  to  be  known. 
Supposing  p  =  0.815,  then  the  maximum  useful  available 
power  will  be  244  H.P. 

Let  us  again  examine  the  diagram  A  =  /(1. 47  A)  (Fig. 
238).  For  our  airplane  at  the  point  corresponding  to  244 
H.P.  on  the  scale  of  powers,  draw  a  perpendicular  to  meet 
tangent  t  in  B  drawn  from  the  diagram  parallel  to  the  scale 
of  velocities.  From  B  draw  the  parallel  BC  to  the  scale  of 
powers.  Point  C  gives  the  maximum  theoretical  load 
which  the  airplane  could  hft,  and  which  in  our  case  would 
be  about  7300  lb.  The  corresponding  velocity  is  measured 
by  segment  BD  which,  read  on  the  scales  of  velocity,  gives 
7  =  132  m.p.h. 

Practically,  however,  the  airplane  cannot  lift  itself  in 
this  condition  as  it  is  necessary  to  have  a  certain  excess 
of  power  in  order  to  leave  the  ground. 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS     375 


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376  AIRPLANE  DESIGN  AND  CONSTRUCTION 

Supposing  then  we  fix  the  condition  that  the  airplane 
should  be  able  to  sustain  itself  at  a  height  of  10,000  ft.     As 

H  =  60,720  log  ^ 

for  H  =  10,000  we  will  have  m  =  0.085,  therefore  in  this 
case  the  useful  power  becomes  0.815X0.685X300  =  167.5 
H.P.  Let  us  then  draw  a  perpendicular  from  A'  corre- 
sponding to  167.5  H.P.  to  meet  tangent  t  in  B'.  From  B' 
draw  the  parallel  to  the  scale  of  power.  From  origin  0 
of  the  diagram  draw  a  segment  00'  parallel  to  the  scale  of 
M  and  which  measures  ^  =  0.685;  from  0'  raise  the  per- 
pendicular until  it  meets  the  horizontal  line  in  C  drawn 
from  BB';  from  C  draw  the  parallel  to  00'  up  to  C"; 
this  point  defines  the  value  of  the  maximum  load  which 
our  airplane  could  lift  up  to  10,000  ft.  and  which  in  our 
case  is  about  4100  lb.  The  corresponding  velocity  is 
measured  by  B'D  and  is  equal  to  116  m.p.h. 

Let  us  now  study  what  the  effect  would  be  of  a  diminu- 
tion of  the  lifting  surface.  Until  now  we  had  supposed 
that  A  =265  sq.  ft.;  that  is,  we  had  a  load  of  8  lb.  per 
sq.  ft.  Now  supposing  this  load  is  increased  up  to  10, 
12,  14,  and  16  lb.  per  sq.  ft.  respectively;  that  is,  the 
lifting  surface  is  reduced  from  265  sq.  ft.  to  214,  178,  153 
and  134  sq.  ft.  successively.  For  each  of  such  hypotheses 
it  will  be  necessary  to  calculate  the  new  values  of  A  and  A ; 
the  results  of  these  calculations  are  grouped  in  Table  47. 
By  means  of  this  table  the  diagrams  of  Fig.  239  have 
been  drawn;  let  us  then  suppose  that  in  each  case  a  pro- 
peller having  the  maximum  efficiency  of  0.815  has  been 
adopted.  The  useful  power  will  be  244  H.P. ;  drawing  from 
A,  the  point  which  corresponds  to  this  power,  the  parallel 
p  to  the  scale  of  velocity,  on  the  intersection  with  this  line 
and  the  diagram  we  shall  have  the  point  which  defines  the 
maximum  velocities;  drawing  the  tangent  t  parallel  to  the 
scale  of  V  from  each  of  the  various  curves  the  points 
of  tangency  which  determine  the  minimum  velocities  will 
be  obtained. 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS      377 


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378 


AIRPLANE  DESIGX  AND  CONSTRUCTION 


Table  47 


<r  =  132.5 


sq.  ft. 


X 

5 

265 

A 

A 

214 

A 
A 

178 

A 
A 

153 

A 

134 

A 

A 

2.3 

0.41 

0.061 
241.0X10- 

0.049 
220.5X10- 

0.041 
205.5X10- 

0.035 
195.0X10- 

0.031 
187.5X10- 


4.0  6.0  8.0 

0.42  0.43  0.47 

0.106  0.159        I        0.212 

244.0X10-<  246.0X10-*  257.0X10" 

0.086  0.128  0.171 

222.5X10-*  225. 0X10-«  233. 5X10- 

0.071  0.107        I        0.143 

207.5X10-«|209.5X10-;216.5X10- 

0.061  0.092  0.122 

197.0X10-*  198.0X10-*  204.5X10" 

0.054        I        0.081  0,107 

189.0X10-*  190.5X10-<  195.5X10- 


10.0  I        11.4 

0.53        I  0.60 

0.265     1  0.302 

274.0X10-<  291.0X10- 
;  0.214  0.24' 

246. 5X10-«  261. 5X10- 
0.178  0.203 

227.5X10-<  239.5X10- 
0.153     ,  0.174 

213.5X10-'224.5X10- 
0.134  0.153 

204.0X10-<  213.0X10- 


A,  sq.  ft.    1       i 

5° 

6° 

70 

S° 

9° 

X 

13.0 

;        14.5 

16.0 

17.8 

19.2 

s 

0.73 

0.88 

1.08 

1.32 

1.57 

265 1 

A 

0.344 

1          0 . 384 

0.423 

0.472 

0.509 

A 

326.0X10-< 

365.  OX  10-* 

428.  OX  10-* 

483.  OX  10-* 

550.  OX  10-* 

214 1 

A 

0.278 

0.310 

0.342 

0.381 

0.411 

A 

288. 5 X 10-* 

321.  5  X  10-* 

364. 5  X  10-* 

415.5X10-* 

469.  5 X  10-* 

178 

A 

0.232 

0.258 

0.285 

0.318 

0.342 

A 

262.5X10-* 

289.  5  X  10-* 

324. 5  X  10-* 

367.  5  X  10-* 

412.5X10-* 

153 

A 

0.199 

0.222 

0.245 

0.272 

0.293 

A 

244.OX10-* 

267.  5  X  10-* 

297. 5  X  10-* 

334. 5  X  10-* 

372. 5  X  10-* 

- 1 

A 

0.174 

0.195 

0.215 

0.238 

0.257 

A 

230.5X10-1 

250. 5  X 10-* 

279.  5 X  10-* 

309. 5  X  10-* 

343.5X10-* 

Table  48  gives  the  values  of  the  maximum  and  mini- 
mum velocities  corresponding  to  the  various  wing  surfaces. 
This  table  sustains  the  point  that  while  a  reduction  of 
surface  increases  the  maximum  velocities,  it  also  increases 
the  values  of  the  minimum  velocities.  Figure  239  also 
clearly  shows  that  a  diminution  of  surface  requires  an 
increase  in  the  minimum  power  necessary  for  flying,  and 
therefore  a  diminution  in  the  climbing  velocity  and  in  the 
ceiling. 


Table 

48 

A 

265 

214 

178 

153 

134 

F(max.) 

156 

158 

1 

162 

164 

166 

F(min.) 

72 

74 

77 

82 

88 

CHAPTER  XXI 

SAND  TESTS— WEIGHING— FLIGHT  TESTS 

I 

The  ultimate  check  on  static  computations  giving  the 
resistance  to  the  various  parts  of  the  airplane,  is  made  either 
by  tests  to  destruction  of  the  various  elements  of  the  struc- 
ture or  by  static  tests  upon  the  machine  as  a  whole. 

In  general  it  is  customary  to  make  separate  tests  (A) 
on  the  wing  truss,  {B)  on  the  fuselage  (C)  on  the  landing 
gear  and  (D)  on  the  control  system, 

A.  Sand  Tests  on  the  Wing  Truss. — Two  sets  of  tests 
are  usually  made  on  a  wing  truss  to  determine  its  strength; 
one  assuming  the  machine  loaded  as  in  normal  flight,  the 
other  loaded  as  in  inverted  flight. 

In  the  first  assumption,  the  inverted  machine  is  loaded 
with  sand  bags,  so  that  the  weight  of  the  sand  exerts  the 
same  action  on  the  wings  as  the  air  reaction  does  in  flight; 
in  the  second  assumption  the  machine  is  loaded  with  sand 
bags  in  the  normal  flying  position.  In  both  cases  the 
machine  is  placed  so  as  to  have  an  inclination  of  25  per 
cent.  (Fig.  240),  so  that  weight  W,  with  its  component  L 
stresses  the  vertical  trusses,  and  with  its  component  D 
stresses  the  horizontal  trusses. 

During  the  test,  the  fuselage  is  supported  by  special 
trestles,  constructed  so  as  not  to  interfere  with  the  deforma- 
tion of  the  wing  truss.  The  distribution  of  the  load  upon 
the  wings  must  be  made  in  such  a  manner  that  the  reactions 
on  the  spars  will  be  in  the  same  ratio  as  those  assumed  in 
the  computation.  For  the  example  of  the  preceding  chap- 
ters it  is  well  to  remember  that  these  reactions  were  due 
to  the  following  loading : 

Upper  front  spar 1.98  lb.  per  linear  inch. 

Upper  rear  spar 1.82  lb.  per  linear  inch. 

Lower  front  spar 1.75  lb.  per  linear  inch. 

Lower  rear  spar 1.62  lb.  per  linear  inch. 

379 


380  AIRPLANE  DESIGN  AND  CONSTRUCTION 


DETERMINATION  OF  THE  FLYING  CHARACTERISTICS     381 

The  sand  is  usually  contained  in  bags  of  various  dimen- 
sions, not  exceeding  a  weight  of  25  lb.  in  order  to  facilitate 

UPPER    RIB 


LOADS   IN  POUNDS 


LOWER     RIB. 


15     35     35     30     30     25     tO     20     20      10      10      10      lO      5       5       5 


hW+l=UJ-U-U 


LOADS  IN  POUNDS. 
Fig.  241. 


handling.     These  sand  bags  must  be  so  placed  that  beside 
satisfying  the  preceding  conditions,  they  give  a  loading 


382 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


diagram  for  the  upper  and  lower  rib  analogous  to  those 
shown    in    Fig.    241    a,  b. 

In  these  figures,  below  the  theoretical  diagrams,  the 
practical  loading,  using  sand  bags  of  5,  10  and  25  lb.  has 
been  sketched.  In  the  test  corresponding  to  normal  flight, 
the  machine  being  inverted,  it  is  necessary  to  consider  the 
weight  of  the  wing  truss,  which  gravitates  upon  the  verti- 
cal trusses  and  therefore  must  be  added  to  the  weight  of 
the  sand,  while  in  actual  flight  it  has  an  opposite  direction 
to  the  air  reaction. 

These  weights  must  be  taken  into  consideration  in  deter- 
mining the  sand  load  corresponding  to  a  coefficient  of  1. 

Before  starting  a  static  test  it  is  customary  to  prepare  a 
diagram  of  each  wing  with  a  table  showing  the  loads  corre- 
sponding to  the  various  coefficients.  For  the  airplane  of 
our  example,  these  diagrams  are  shown  in  Figs.  242  and 
243,  and  tables  49  and  50. 


UPPER 
WINO 


4--E48m  — 
4—24  811 


Fig.  242. 
Table  49 


Factor 
safety 

Table 

of  loads  for  sand  test 

3 

235 

255 

255 

220 

220 

255 

270 

4 

305 

345 

345 

300 

300 

345 

360 

5 

390 

435 

435 

375 

375 

435 

455 

6 

475 

525 

525 

455 

455 

525 

540 

7 

560 

610 

610 

520 

520 

610 

635 

8 

640 

700 

700 

615 

615 

700 

725 

9 

720 

790 

790 

690 

690 

790 

820 

10 

800 

875 

875 

760 

760 

875 

905 

SAND  TESTS— WEIGHING— FLIGHT  TESTS 


383 


240  ■        g'V.O  I        gO-3       I       20.9        I        24.0 


!■    ■^""'     !■ 


LOWER 
VVING. 


Fig.  243 
Table  50 


Factor 
safety 

Table  of  loads  for  san 

d  test 

3 

130 

225 

225 

195 

195 

225 

165 

4 

170 

305 

305 

270 

270 

305 

215 

5 

210 

385 

385 

335 

335 

385 

275 

6 

260 

460 

460 

405 

405 

460 

330 

7 

300 

540 

540 

470 

470 

540 

390 

8 

345 

620 

620 

540 

540 

620 

440 

9 

390 

700 

700 

615 

615 

700 

500 

10 

440 

780 

780 

690 

690 

780 

560 

During  the  progress  of  the  test  it  is  of  maximum  im- 
portance to  measure  the  deformation  to  which  the  spars 
are  subjected  in  order  to  determine  their  elastic  curves 
under  various  loadings.  In  general  the  determination  of  an 
elastic  curve  below  a  coefficient  of  3  is  disregarded,  as 
the  deformations  are  very  small.  To  measure  the  defor- 
mations small  graduated  rulers  are  usually  attached  to  the 
spars  in  front  of  which  a  stretched  copper  wire  is  kept 
as  a  reference  line.  Naturally,  before  applying  the  load, 
it  is  necessary  to  take  a  preliminary  reading  of  the  inter- 
sections of  the  graduated  rulers  with  the  copper  wire,  so  as 
to  compute  the  effective  deformation.  Then  proceed  as 
follows : 

1.  Start  loading  the  sand  bags  on  the  wings,  following 
the  preceding  instructions  for  a  total  load  corresponding 
to  a  coefficient  of  3,  minus  the  weight  of  the  wing  truss. 


384  AIRPLANE  DESIOX  AND  CONSTRUCTION 

2.  When  this  entire  load  has  been  plaeecl  on  the  wings, 
take  a  reading  of  all  the  rulers. 

3.  Unload  the  wing  truss  gradually  and  completel3^ 

4.  Take  a  new  reading  with  the  machine  unloaded. 

5.  Load  the  machine  again  so  as  to  reach  a  total  load 
equal  to  four  times  that  corresponding  to  a  coefficient  of  1 
minus  the  weight  of  the  wing  truss. 

6.  Take  another  reading. 

7.  Unload  the  machine  completely. 

8.  Take  another  reading  with  the  machine  unloaded. 
And  so  on  for  coefficients  of  5,  6,  7,  etc. 

As  the  maximum  coefficient  for  which  the  machine  has 
been  computed,  and  that  corresponding  to  which  the  ma- 
chine will  break,  is  approached,  it  is  not  safe  to  take 
further  readings  as  the  falling  of  the  load  which  follows 
the  breaking  may  endanger  the  observer.  The  various 
readings  of  the  deformations  with  the  load  and  those  after 
unloading,  are  usually  put  in  tabular  forms  and  serve  as  a 
basis  for  plotting  the  elastic  curves.  Furthermore  the 
deformations  with  the  load,  allow  the  computation  of 
deformations  sustained  both  by  struts  and  diagonals. 
Consequently  all  the  elements  are  obtained  by  means  of 
which  the  unit  stresses  in  the  various  parts  of  the  wing 
truss  under  difTerent  loadings  can  be  computed. 

B.  Sand  Test  of  the  Fuselage. — In  computing  the  fusel- 
age, it  was  scon  that  the  principal  stresses  are  those  pro- 
duced in  flight.  Therefore  the  fuselage  sand  test  is  usually 
made  b}^  suspending  it  by  the  four  fittings  of  the  main 
diagonals  of  the  wings,  and  subsequently  loading  it  with 
sand  bags  and  lead  weights  so  as  to  produce  loads  equal  to  3, 
4,  5,  etc.,  times  the  weight  of  the  various  masses  contained 
in  the  fuselage.  For  the  determination  of  the  coefficient  of 
safety  the  sum  of  the  w^eights  of  these  masses  is  taken  as  a 
basis.  At  the  same  time  a  load  equal  to  the  breaking  load 
of  the  elevator  itself  is  placed  corresponding  to  the  point 
at  which  the  elevator  is  fixed;  to  equilibrate  the  moment 
due  to  this  load  the  usual  procedure  is  to  anchor  the  forward 
portion  of  the  fuselage.  Fig.  244  clearly  shows  how  the 
test  is  prepared 


SAND   TESTS— WEIGHING— FLIGHT  TESTS 


385 


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1 

1 

^ 

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1 

1 
1 

1 

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5 

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s: 

386  AIRPLANE  DESIGN  AND  CONSTRUCTION 

C.  Sand  Test  of  the  Landing  Gear. — This  is  done  with 
the  hmding  gear  in  a  position  corresponding  to  the  hne  of 
flight  and  by  loading  it  with  lead  weights. 

The  load  assumed  as  a  basis  for  the  determination  of  the 
coefficient  is  taken  equal  to  the  total  weight  of  the  airplane 
with  full  load.  If,  corresponding  to  each  value  of  load  W, 
the  corresponding  vertical  deformation  /  is  determined,  it  is 
possible  to  plot  the  diagram  of  W  as  a  function  of  /,  whose 
area  y  W  df  gives  the  total  work  the  shock  absorbing  system 
is  capable  of  absorbing. 

D.  Sand  Test  of  Control  Surfaces. — This  test  is  made 
with  the  control  surfaces  mounted  on  the  fuselage,  and 
loaded  with  the  criterion  explained  in  Chapter  XVIII. 

II 

Weighing  the  Airplane. — The  weighing  of  the  airplane  is 
necessary  not  only  to  determine  whether  the  effective 
weights  correspond  to  the  assumed  ones,  but  also  to  deter- 
mine the  position  of  the  center  of  gravity  both  with  full 
load  and  with  the  various  hypothesis  of  loading  which  may 
happen  in  flight. 

The  center  of  gravity  is  contained  in  the  plane  of  sym- 
metry of  the  airplane.  To  determine  this  it  suffices  to 
determine  two  vertical  lines  which  contain  it,  and  for  this 
it  is  only  necessary  to  weigh  the  aeroplane  twice,  the  first 
time  with  the  tail  on  the  ground  (Fig.  245),  and  the  second 
time  with  the  nose  of  the  machine  on  the  ground  (Fig. 
246).  Three  scales  are  necessary  for  each  weighing,  two 
under  the  wheels,  and  one  under  the  tail  skid  for  the  case 
of  Fig.  245,  and  under  the  propeller  hub  for  the  case  of 
Fig.  246. 

Using  W  and  W"  to  denote  the  weights  read  on  the 
scales  under  the  wheels  and  W"  for  that  read  on  the  scale 
supporting  the  tail  skid,  the  total  weight  will  be 

W  =  W  +  W"  +  W" 
The  vertical  axis  v'  passing  through  the  center  of  gravity 
divides  the  distance  I  between  the  axis  of  the  wheels  and 


SAND  TESTS— WEIGHING— FLIGHT  TESTS 


387 


388  AIRPLANE  DESIGN  AND  CONSTRUCTION 

the  point  of  .support  of  the  tail  skid  into  two  parts  Xi  and 
X2  so  that 

xi  ^         W_''  __ 

X2        W'  +  W" 


Fio.  24G. 


for  which 


Xx 


V/' 


xi  +  X2       W  +  W"  +  W 


SAND  TESTS— WEIGHING— FLIGHT  TESTS 


389 


390  AIRPLAXE  DESIGN  AXD  CONSTRUCTION 

and  since 


Xi  +  x.>  =  I  and  W  +  W"  +  W" 
we  shall  ha\'e 


W 


Xi  =-  IX 


W 


Let  us  proceed  analogously  for  the  case  of  Fig.  240.  In 
this  manner  two  lines  v'  and  v"  are  obtained  whose  inter- 
section defines  the  center  of  gravity. 

To  eliminate  eventual  errors  and  to  obtain  a  check  on  the 
work  it  is  convenient  to  determine  the  third  line  v'",  by 


/     \ 


Fig.   248 

balancing  the  machine  on  the  wheels;  v'"  will  then  be  the 
vertical  which  passes  through  the  axis  of  the  wheels  (Fig. 
247).  The  three  Unes  v',  v"  and  v'"  must  meet  in  a  point 
(Fig.  248). 

Ill 

The  flight  tests  include  two  categories  of  tests,  that  is; 

A.  Stability  and  maneuverability  tests. 

B.  Efficiency  test. 

A.  The  purpose  of  the  stability  tests  is  to  verify  the 
balance  of  aeroplane  when  (a)  flying  with  engine  going, 
and  when  volplaning,  (h)  in  normal  flight  and  during 
maneuvers. 

Chapter  XI  has  stated  the  necessary  requisites  for  a  well- 
balanced  airplane,  therefore  a  repetition  need  not  be  given. 


SAND  rESTS^WEIGHINa^FLIGHT  TESTS 


391 


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392  AIRPLANE  DESIGN  AND  CONSTRUCTION 

The  same  may  be  said  of  maneuverability  tests,  whose 
scope  is  to  verify  the  good  and  rapid  maneuverabihty  of  the 
airplane  without  an  excessive  effort  by  the  pilot. 

B.  The  scope  of  the  efhciency  tests  is  to  determine  the 
flying  characteristics  of  the  airplane,  that  is,  the  ascensional 
and  horizontal  velocities  corresponding  to  various  loads  and 
types  of  propellers  which  might  eventually  be  wanted  for 
experiments. 

Table  51  gives  examples  of  tables  that  show  which  factors 
of  the  efficiency  tests  are  the  most  important  to  determine. 


APPENDIX 

The  following  tables  are  given  for  the  convenience  of  the 
designer:  Tables  52,  53,  54,  55  and  56  giving  the  squares 
and  cubes  of  velocities.  Table  57  giving  the  cubes  of  revolu- 
tions per  minute  and  per  second.  Table  58  giving  the  5th 
powers  of  the  diameters  in  feet. 


Table  52. — T.\ble  of  Squares  and  Cubes  of  Velocities 


V 

y2 

V3 

Miles  per 
hr. 

Ft.  per  sec. 

Miles  per  hr. 

Ft.  per  sec. 

Miles  per  hr. 

Ft.  per  sec. 

50 

73.33 

2,500 

5,377.7 

125,000 

394,430 

51 

74.80 

2,601 

5,595.0 

132,651 

418,510 

52 

76.27 

2,704 

5,817.1 

140,608 

443,670 

53 

77.73 

2,809 

6,042.0 

148,877 

469,640 

54 

79.20 

2,916 

6,272.6 

157,464 

496,790 

55 

80.67 

3,025 

6,507.6 

166,375 

524,970 

56 

82.13 

3,136 

6,745.3 

175,616 

553,990 

57 

83.60 

3,249 

6,988.9 

185,193 

584,280 

58 

85.07 

3,364 

7,237.0 

195,112 

614,270 

59 

86.53 

3,481 

7,487.5 

205,379 

647,890 

60 

88.00 

3,600 

7,744.0 

216,000 

681,470 

61 

89.47 

3,721 

8,004.9 

226,981 

716,200 

62 

90.93 

3,844 

8,268.2 

238,328 

751,830 

63 

92.40 

3,969 

8,537.8 

250,047 

788,890 

64 

93.87 

4,096 

8,811.8 

262,144 

827,140 

65 

95.33 

4,225 

9,087.8 

274,625 

866,340 

66 

96.80 

4,356 

9,370.2 

287,496 

907,040 

67 

98.27 

4,489 

9,657.0 

300,763 

948,990 

68 

99.73 

4,624 

9,946.0 

314,432 

991,920 

69 

101.02 

4,761 

10,205.0 

328,509 

1,030,920 

70 

102.67 

4,900 

10,541.0 

343,000 

1,082,260 

71 

104 . 13 

5,041 

10,843.0 

357,911 

1,129,090 

72 

105.60 

5,184 

11,152.0 

373,248 

1,177,580 

73 

107.07 

5,329 

11,464.0 

389,017 

1,227,450 

74 

108.53 

5,476 

11,779.0 

405,224 

1,278,350 

75 

110.00 

5,625 

12,100.0 

421,875 

1,331,000 

76 

111.47 

5,776 

12,426.0 

438,976 

1,385,080 

77 

112.93 

5,929 

12,753.0 

456,533 

1,440,220 

78 

114.40 

6,084 

13,088.0 

474,552 

1,497,200 

79 

115.87 

6,241 

13,426.0 

493,039 

1,555,654 

80 

117.33 

6,400 

13,766.0 

512,000 

1,615,203 

393 


394 


AIRPLANE  DESIGN  AND  CONSTRUCTION 


Table  53. — T^vble  of  Squauk;:;  and  Cubes  of  Velocities 


V 

^ 

■J 

I 

-3 

Miles  per 
hr. 

Ft.  per  see. 

Miles  per  hr. 

Ft.  per  sec. 

Miles  per  hr. 

Ft.  per  sec. 

81 

118.80 

6,561 

14,113 

531,441 

1,076,680 

82 

120.27 

6,724 

14,465 

551,368 

1,739,690 

83 

121.73 

6,889 

14,818 

571,787 

1,803,820 

84 

123.20 

7,056 

15,178 

592,704 

1,869,960 

85 

124.67 

7,225 

15,543 

614,125 

1,937,700 

86 

126.13 

7,396 

15,909 

636,050 

2,006,570 

87 

127.60 

7,569 

16,282 

658,503 

2,077,550 

88 

129.07 

7,744 

16,659 

681,472 

2,150,190 

•89 

130.53 

7,921 

17,038 

704,960 

2,224,000 

90 

132.00 

8,100 

17,424 

729,000 

2,299,970 

91 

133.47 

8,2S1 

17,814 

753,571 

2,377,670 

92 

134.93 

8,464 

18,206 

778,688 

2,456,550 

93 

136.40 

8,649 

18,605 

804,357 

2,537,720 

94 

137.87 

8,836 

19,008 

830,584 

2,620,650 

95 

139.33 

9,025 

19,413 

857,375 

2,704,800 

96 

140.80 

9,216 

19,825 

884,736 

2,791,310 

97 

142.27 

9,409 

20,241 

912,673 

2,879,650 

98 

143.73 

9,604 

20,658 

941,192 

2,969,220 

99 

145.20 

9,801 

21,083 

970,299 

3,061,260 

100 

146.67 

10,000 

21,512 

1.000,000 

3,155,180 

101 

148.13 

10,201 

21,943 

1,030,301 

3,250,340 

102 

149.60 

10,404 

22,380 

1,061,208 

3,348,070 

103 

151.07 

10,609 

22,822 

1,092,727 

3,447,750 

104 

152 . 53 

10,816 

23,265 

1,124,864 

3,548,670 

105 

154 . 00 

11,025 

23,716 

1,157,625 

3,652,260 

106 

155.47 

11,236 

24,171 

1,191,016 

3,757,850 

107 

156.93 

11,449 

24,627 

1,225,043 

3,864,720 

108 

158.40 

11,664 

25,091 

1,259,712 

3,974,340 

109 

159.87 

11,881 

25,558 

1,295,029 

4,086,030 

110 

161.33 

12,100 

26,027 

1,331,000 

4,199,000 

APPENDIX  395 

Table  54. — Table  of  Squares  and  Cubes  of  Velocities 


r 

1-2 

T'3 

Miles  per 
hr. 

Ft.  per  sec. 

Miles  per  hr. 

Ft.  per  sec. 

Miles  per  hr. 

Ft.  per  sec. 

Ill 

162.80 

12,321 

26,504 

1,367,631 

4,314,820 

112 

164.27 

12,544 

26,C85 

1,404,928 

4,432,770 

113 

165.73 

12,769 

27,466 

1,442,897 

4,552,010 

11-1 

167.20 

12,996 

27,C56 

1,481,544 

4,674,220 

115 

168.07 

13,225 

28,450 

1,520,875 

4,708,580 

116 

170.13 

13,456 

28,944 

1,560,8C6 

4,924,790 

117 

171.60 

13,689 

20,447 

1,601,613 

5,053,080 

118 

173.07 

13,924 

29,953 

1,643,032 

5,184,000 

119 

174.53 

14,161 

30,461 

1,685,159 

5,316,310 

120 

176.00 

14,400 

30,976 

1,728,CC0 

5,451,780 

121 

177.47 

14,641 

31,496 

1,771,561 

5,589,520 

122 

178.93 

14,884 

32,016 

1,815,848 

5,728,620 

123 

180.40 

15,129 

32,544 

1,860,867 

5,870,^60 

124 

181.87 

15,376 

33,077 

1,906,624 

6,015,060 

125 

183.33 

15,625 

33,610 

1,953,125 

6,161,700 

126 

184.80 

15,876 

34,151 

2,000,376 

6,311,120 

127 

186.27 

16,129 

34,697 

2,048,383 

6,462,C20 

128 

187.73 

16,384 

35,243 

2,097,152 

6,616,080 

129 

189.20 

16,641 

35,797 

2,140,689 

6,772,720 

130 

190.67 

16,900 

36,355 

2,197,000 

6,931,820 

131 

192.13 

17,161 

36,914 

2,248,0!;  1 

7,0:2,280 

132 

193 . 60 

17,424 

37,481 

2,299,968 

7,256,320 

133 

195.07 

17,689 

38,052 

2,352,637 

7,422.860 

134 

196.53 

17,956 

38,624 

2,406,104 

7,500,7tO 

135 

198.00 

18,225 

39,204 

2,460,375 

7,762,3£0 

136 

199.47 

18,496 

39,788 

2,515,456 

7,936,570 

137 

200.93 

18,769 

40,373  . 

2,571,353 

8,112,120 

138 

202.40 

19,044 

40,966 

2,628,072 

8,291,470 

139 

203.87 

19,321 

41,563 

2,685,619 

8,473,440 

140 

205.33 

19,600 

42,160 

2,744,000 

8,656,800 

^') 


396 


AIRPLAXK  DESIGN  AND  CONSTRUCTION 


Tablk  55. — Tahi.k  of  Squares  axd  Cubes  or  Velocities 


Miles  per 
hr. 


Ft.  per  sec. 


Miles  per  hr.        Ft.  per  sec. 


Miles  per  hr. 


Ft.  per  sec. 


141 

206.80 

19,881 

42,760 

2,803,221 

8,844,050 

142 

208.27 

20,164 

43,376 

2,863,288 

9,034,000 

143 

209.73 

20,449 

43,987 

2,924,207 

9,225,330 

144 

211.20 

20,736 

44,605 

2,985,984 

9,420,670 

145 

212.67 

21,025 

45,229 

3,048,625 

9,618,750 

146 

214.13 

21,316 

45,852 

3,112,136 

9,818,220 

147 

215.60 

21,609 

46,483 

3,176,523 

10,021,800 

148 

217.07 

21,904 

47,119 

3,241,792 

10,228,200 

149 

218.53 

22,201 

47,755 

3,307,949 

10,435,900 

150 

220.00 

22,500 

48,400 

3,375,000 

10,648,000 

151 

221.47 

22,801 

49,049 

3,142,951 

10,862,800 

152 

222.93 

23,104 

49,698 

3,511,808 

11,079,100 

153 

224.40 

23,409 

50,355 

3,581,577 

11,279,500 

154 

225.87 

23,716 

51,017 

3,652,264 

11,523,300 

155 

227.33 

24,025 

51,679 

3,723,875 

11,748,200 

156 

228.80 

24,336 

52,349 

3,796,416 

11,977,600 

157 

230.27 

24,649 

53,024 

3,869,893 

12,209,900 

158 

231.73 

24,964 

53,699 

3,944,312 

12,443,600 

159 

233.20 

25,281 

54,382 

4,019,679 

12,682,000 

160 

234.67 

25,600 

55,070 

4,096,000 

12,923,300 

161 

236.13 

25,921 

55,757 

4,173,281 

13,166,000 

162 

237.60 

26,244 

56,454 

4,251,528 

13,725,800 

163 

239.07 

26,569 

57,154 

4,330,747 

13,663,900 

164 

240.53 

26,896 

57,855 

4,410,944 

13,915,800 

165 

242.00 

27,225 

58,564 

4,492,125 

14,172,500 

166 

243.47 

27,556 

59,278 

4,574,296 

14,432,300 

167 

244.93 

27,889 

59,991 

4,657,463 

14,693,400 

168 

246.40 

28,224 

60,713 

4,741,632 

14,959,600 

169 

247 . 87 

28,561 

61,440 

4,826,809 

15,229,000 

170 

249.33 

28,900 

62,166 

4,913,000 

15,499,700 

APPENDIX 
Table  56.— Table  of  Square.s  and  Cubes  of  Velocities 


397 


Miles  ; 

hr. 


171 

172 

173 

174 

175 

176 

177 

178 

179 

180 

181 

182 

183 

184 

185 

186 

187 

188 

189 

190 

191 

192 

193 

194 

195 

196 

197 

198 

199 

200 


Ft.  per  sec. 

Miles  per  hr. 

Ft.  per  sec. 

'    Miles  per  hr. 

1 

1     Ft.  per  sec. 

250.80 

29,241 

62,901 

5,000,211 

15,775,800 

252.27 

29,584 

63,640 

5,088,448 

16,054,500 

253.73 

29,929 

64,379 

5,177,717 

16,334,850 

255.20 

30,276 

65,127 

5,268,024 

16,620,500 

256 . 67 

30,625 

65,880 

5,359,375 

16,908,500 

258.13 

30,976 

66,631 

5,451,776 

17,199,500 

259.60 

31,329 

67,392 

5,545,233 

17,495,000 

261.07 

31,684 

68,158 

5,639,752 

17,794,000 

262 . 53 

32,041 

68,922 

5,735,339 

18,094,300 

264.00 

32,400 

69,696 

5,832,000 

18,399,800 

265 . 47 

32,761 

70,474 

5,929,741 

18,709,800 

266 . 93 

33,124 

71,252 

6,028,568 

19,029,750 

268.40 

33,489 

72,038 

6,128,487 

19,335,400 

269.87 

33,856 

72,830 

6,229,504 

19,655,500 

271.33 

34,225 

73,620 

6,331,625 

19,975,500 

272.80 

34,596 

74,420 

6,434,856 

20,301,900 

274.27 
275.73 

34,969 
35,344 

75,224 
76,027 

6,539,203 
6,644,672 

20,631,500 
20,962,900 

277.20 

35,721 

76,840 

6,751,269 

21,300,000 

278.67 

36,100 

77,657 

6,859,000 

21,640,750 

280.13 

36,481 

78,473 

6,967,871 

21,982,500 

281 . 60 

36,864 

79,299 

7,077,888 

22,330,500 

283.07 

37,249 

80,129 

7,189,057 

22,682,000 

284 . 53 

37,636 

80,957 

7,301,384 

23,034,750 

286.00 

38,025 

81,796 

7,414,875 

23,393,500 

287.47 

38,416 

82,639 

7,529,536 

23,756,000 

288 . 93 

38,809 

83,481 

7,645,373 

24,120,000 

290 . 40 

39,204 

84,332 

7,762,392 

24,490,850 

291.86 

39,601 

85,182 

7,880,599 

24,861,500 

293.33 

40,000 

86,043 

8,000,000 

25,239,000 

398  AIRPLAXE  DESIGN  AND  CONSTRUCTION 

Table  57. — Table  of  Cubes  op  R.p.m.  and  R.p.s 


Per  min 

Per  sec. 

Per  min. 

Per  sec. 

500 

8.33 

125.0X10" 

578.7 

550 

9.17 

166.4X10" 

768.5 

600 

10.00 

216.0X10" 

1,000.0 

650 

10.83 

274.6X10" 

1,271.4 

700 

11.67 

343 . 0  X 10" 

1,588.0 

760 

12.50 

421.9X10" 

1,953.3 

800 

13.33 

512.0X10" 

2,370.4 

850 

14.17 

614.1X10" 

2,843.2 

900 

15.00 

729 . 0  X 10" 

3,375.0 

950 

15.83 

857.4X10" 

3,969.4 

1,000 

16.67 

1,000.0X10" 

4,629.6 

1,050 

17.50 

1,157.6X10" 

5,359.1 

1,100 

18.33 

1,331.0X10" 

6,162.0 

1,150 

19.17 

1,520.0X10" 

7,025.0 

1,200 

20.00 

1,728.0X10" 

8,000.0 

1,250 

20.83 

1,953.1X10" 

9,042.1 

1,300 

21.67 

2,197.0X10" 

10,171.0 

1,350 

22.50 

2,460.4X10" 

11,364.0 

1,400 

23.33 

2,744.0X10" 

12,704.0 

1,450 

24.17 

3,048.6X10" 

14,114.0 

1,500 

25.00 

3,375.0X10" 

15,625.0 

1,550 

25.83 

3,723.9X10" 

17,241.0 

1,600 

26.67 

4,096.0X10" 

18,963.0 

1,650 

27.50 

4,492.1X10" 

20,797.0 

1,700 

28.33 

4,913.0X10" 

22,746.0 

1,750 

29.17 

5,359.4X10" 

24,812.0 

1,800 

30.00 

5,832.0X10" 

27,000.0 

1,850 

30.83 

6,331.6X10" 

29,313.0 

1,900 

31.67 

6,859.0X10" 

31,7r)5.0 

1,950 

32.50 

7,414.9X10" 

34,329.0 

2,000 

33.33 

8,000.0X10" 

37,037.0 

2,050 

34.17 

8,615.1X10" 

39,885.0 

2,100 

35.00 

9,261.0X10" 

42,874.0 

2,150 

35.83 

9,938.4X10" 

46,011.0 

2,200 

36.67 

10,648.0X10" 

49,296.0 

2,250 

37.50 

11,390.6X10" 

52,736.0 

2,300 

38.33 

12,167.0X10" 

56,329.0 

2,350 

39.17 

12,977.9X10" 

60,083.0 

2,400 

40.00 

13,82 1.  OX  10" 

64,000.0 

2,450 

40.83 

14,706.1X10" 

68,084.0 

2,500 

41  67 

15.625.  OXIO'-' 

72,338.0 

APPENDIX 


399 


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INDEX 


Aerodynamical  Laboratory,  90 
Aerodynamics,  elements  of,  87,-101 
Ailerons,  33 

construction  of,  35 
Air  pump  pressure  feed,  58 
Aluminum,  234 
ses  of,  234 
Angle  of  drift,  89 

of  incidence,  89 
Axis,  direction,  19 

pitching,  19 

principal,  19 

rolling,  19 


B 


Banking,  31 

angle  of,  32 
Biplane,  effects  of,  system,  12 

structure,  15 


Cables,  225 

splicing,  226 
Canard  type,  27 
Ceiling,  195-203 
Center  of  gravity,  273 

position  of,  273 
Climbing,  188-203 

influence  of  air  density  on,  189 

speed,  130-133 

time  of,  191-194 
Compressors,  70 
Control  surfaces,  19 

sand  test  of,  286 
Copper,  uses  of,  234 
Cruising  radius,  204-220 

factors  modifying,  214 
Cubes,  tables  of,  393-397 


Dihedral  angle,  35 

Dimensions   of   airplane,    increasing 

the,  209 
Dispersion,  angle  of,  73 
Distribution  of  masses,  21 
Drag,  definition  of,  1 
Drift.  1 


Efficiency,    factors    influencing    lift- 
drag  efficiency,  2 
of  sustaining  group,  102 
problems  of,  161-166 
Elastic  cord,  256-258 

curve    method    of    spar   analy- 
sis, 306-311 
work  absorbed  by,  257-258 
Elevator,  20 

computation,  322 
function,  22 
size  of,  20 
Engine,  51 

center  of  gravity  of,  56 
characteristics  of,  for  airplane, 

51 
function   of,   at  high   altitudes, 

68-71 
types  of,  51 


Fabrics,  247-256 

Fifth  powers  table,  399 

Fin  computation,  314 

Flat  turning,  29 

Flying  characteristic  determination, 

358-378 
Flying  in  the  wind,  151-159 
Flying  tests,  efficiency,  392 


401 


402 


INDEX 


Flyins?  maneuverability,  391 

stability,  390 
Flying  with  power  on,  115-133 
Forces  acting  on  airplane  in  flight,  45 

effect  of,  45-46 
Fuselage,  37-43 

reverse  curve  in,  39 

sand  test  of,  384 

spar  analysis  of,  332 

static  analysis  of,  324-334 

types  of,  39-40 

value  of  A'  for,  39 


Materials  for  Aviation,  221-200 
Metacentric  curve,  137 
Monotoque  fuselage,  39 
Motive  quality,  165 
Mufflers,  ()7 
Multiplane  surfaces,  211 

o 

Oil  tank,  position  of,  58 


Gasoline,  multiple,  tank,  58 
piping  for,  feed,  60 
types  of,  feed,  58-60 

Glide,  102-114 
angle  of,  104 
spiral,  111-114 

Glues,  260 

Great  loads,  204-220 


Incidence,  angle  of,  88-89 

Iron  and  steel  in  aviation,  222-234 


Landing  gear,  44-50 

analysis  of,  334-342 
position  of,  46 
sand  test  of,  386 
stresses  on,  46-47 
type  of,  44 

Leading  edge,  6 
function  of,  6 

Lift,  1 

Lift-drag  ratio,  2 
efficiency  of,  2 
law  of  variation  of,  6 
value  of,  2 

M 

Maneuvrability,  134-150 
Marginal  losses,  10 


Pitot  tube,  91 

Planning  the  project,  261-275 

Pressure  zone,  1 

Principal  axis,  19 

Propeller,  72-85 

efficiency  of,  79-85 

pitch,  74 

profile  of,  blades,  75 

static  analj'sis  of,  342-357 

types  of,  73 

width  of,  blades,  74 

R 

Radiators,  61-67 

types  of,  62 
Resistance  coefficients,  96-98 
Rib  construction,  16 
Rubber  cord,  47-48 

binding  of,  49 

energy  absorbed  Ijy,  47 
Rudder,  36 

balanced,  3() 

static  analysis  of,  315 


Sand  test,  control  surface,  386 

fuselage,  384-385 

landing  gear,  386 

wing  truss,  379-384 
Shock  a])sorbers,  47-48 

uses  of,  47 
Spar  analysis,  276-288 
Speed,  167-187 

means  to  increase,  168 


INDEX 


403 


Spiral  gliding,  111-114 
Squares,  tables  of,  393-397 
Stability,  134-150 

directional,  141 

intrinsic,  147 

lateral,  140 

transversal,  141 

zones  of,  139 
Stabilizer,  computation  of,  322 

dimension  of,  20 

effects  of,  action,  137 

function  of,  20 

mechanical,  147-150 

shape  of,  20 
Static  analysis,  of  control  surfaces, 
315-323 

of  fuselage,  324-334 

of  main  planes,  276-314 
Streamline  wire,  225 
Struts,  fittings,  18 

computations,  294-29(3 

tables,  297-300 
Sustentation  phenomena,  1 
Synchronizers,  73 


Tail  skid,  49,  50 
uses  of,  50 
Tail  system  computations,   314-323 
Tandem  surfaces,  211 
Tangmt  flying,  121 
Tie  rods,  226 

Trailing  edge,  function  of,  9 
Transmission  gear,  56 


Transversal  stability,  30 
Triplane,  effect  of,  sj^stem,  12 
Truss  analysis,  2SS-292 
Tubing,  tables  for  round,  229-231 
table  of  moment  of  inertia  for 
round,  231 
of  weights  for  round,  230 
tables  of  streamline,  232-233 

U 

Unit  loading,  12,  278,  279 
Useful  load  increase,  212 


\'arnishes,  259 

finishing,  259 

stretching,  259 
Veneers,  241-254 

tables  for  Haskelite,  246-254 

^^' 

Weighing  the  airplane,  389 
Wind,  effect  of,  on  stability,  156 
Wing,  analysis  of,  truss,  276 

element  of,  efficiencj^  9 

elements  of,  3 

sand  test  of,  379 

unit  stress  on,  306-314 
Wires,  steel,  tables,  224 

streamline,  225 
Wood,  234-254 

characteristics  of  various,  236- 
239 


Library 
N.  C.  State   College 


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